Single identified hadron spectra from sNN=130GeV Au+Au collisions

transcript

Single Identified Hadron Spectra from√

sNN = 130 GeV Au+Au

Collisions

K. Adcox,40 S.S. Adler,4 N.N. Ajitanand,33 Y. Akiba,14 J. Alexander,33 L. Aphecetche,35

Y. Arai,14 S.H. Aronson,4 R. Averbeck,34 T.C. Awes,27 K.N. Barish,5 P.D. Barnes,19

J. Barrette,21 B. Bassalleck,25 S. Bathe,22 V. Baublis,28 A. Bazilevsky,12, 30 S. Belikov,12, 13

F.G. Bellaiche,27 S.T. Belyaev,16 M.J. Bennett,19 Y. Berdnikov,31 S. Botelho,32

M.L. Brooks,19 D.S. Brown,26 N. Bruner,25 D. Bucher,22 H. Buesching,22 V. Bumazhnov,12

G. Bunce,4, 30 J.M. Burward-Hoy,34 S. Butsyk,34, 28 T.A. Carey,19 P. Chand,3 J. Chang,5

W.C. Chang,1 L.L. Chavez,25 S. Chernichenko,12 C.Y. Chi,8 J. Chiba,14 M. Chiu,8

R.K. Choudhury,3 T. Christ,34 T. Chujo,4, 39 M.S. Chung,15, 19 P. Chung,33 V. Cianciolo,27

B.A. Cole,8 D.G. d’Enterria,35 G. David,4 H. Delagrange,35 A. Denisov,12 A. Deshpande,30

E.J. Desmond,4 O. Dietzsch,32 B.V. Dinesh,3 A. Drees,34 A. Durum,12 D. Dutta,3

K. Ebisu,24 Y.V. Efremenko,27 K. El Chenawi,40 H. En’yo,17, 29 S. Esumi,39 L. Ewell,4

T. Ferdousi,5 D.E. Fields,25 S.L. Fokin,16 Z. Fraenkel,42 A. Franz,4 A.D. Frawley,9

S.-Y. Fung,5 S. Garpman,20, ∗ T.K. Ghosh,40 A. Glenn,36 A.L. Godoi,32 Y. Goto,30

S.V. Greene,40 M. Grosse Perdekamp,30 S.K. Gupta,3 W. Guryn,4 H.-A. Gustafsson,20

J.S. Haggerty,4 H. Hamagaki,7 A.G. Hansen,19 H. Hara,24 E.P. Hartouni,18

R. Hayano,38 N. Hayashi,29 X. He,10 T.K. Hemmick,34 J.M. Heuser,34 M. Hibino,41

J.C. Hill,13 D.S. Ho,43 K. Homma,11 B. Hong,15 A. Hoover,26 T. Ichihara,29, 30

K. Imai,17, 29 M.S. Ippolitov,16 M. Ishihara,29, 30 B.V. Jacak,34, 30 W.Y. Jang,15 J. Jia,34

B.M. Johnson,4 S.C. Johnson,18, 34 K.S. Joo,23 S. Kametani,41 J.H. Kang,43 M. Kann,28

S.S. Kapoor,3 S. Kelly,8 B. Khachaturov,42 A. Khanzadeev,28 J. Kikuchi,41 D.J. Kim,43

H.J. Kim,43 S.Y. Kim,43 Y.G. Kim,43 W.W. Kinnison,19 E. Kistenev,4 A. Kiyomichi,39

C. Klein-Boesing,22 S. Klinksiek,25 L. Kochenda,28 V. Kochetkov,12 D. Koehler,25

T. Kohama,11 D. Kotchetkov,5 A. Kozlov,42 P.J. Kroon,4 K. Kurita,29, 30 M.J. Kweon,15

Y. Kwon,43 G.S. Kyle,26 R. Lacey,33 J.G. Lajoie,13 J. Lauret,33 A. Lebedev,13 D.M. Lee,19

M.J. Leitch,19 X.H. Li,5 Z. Li,6, 29 D.J. Lim,43 M.X. Liu,19 X. Liu,6 Z. Liu,6 C.F. Maguire,40

J. Mahon,4 Y.I. Makdisi,4 V.I. Manko,16 Y. Mao,6, 29 S.K. Mark,21 S. Markacs,8

G. Martinez,35 M.D. Marx,34 A. Masaike,17 F. Matathias,34 T. Matsumoto,7, 41

P.L. McGaughey,19 E. Melnikov,12 M. Merschmeyer,22 F. Messer,34 M. Messer,4

Y. Miake,39 T.E. Miller,40 A. Milov,42 S. Mioduszewski,4, 36 R.E. Mischke,19 G.C. Mishra,10

J.T. Mitchell,4 A.K. Mohanty,3 D.P. Morrison,4 J.M. Moss,19 F. Muhlbacher,34

M. Muniruzzaman,5 J. Murata,29 S. Nagamiya,14 Y. Nagasaka,24 J.L. Nagle,8

Y. Nakada,17 B.K. Nandi,5 J. Newby,36 L. Nikkinen,21 P. Nilsson,20 S. Nishimura,7

A.S. Nyanin,16 J. Nystrand,20 E. O’Brien,4 C.A. Ogilvie,13 H. Ohnishi,4, 11 I.D. Ojha,2, 40

M. Ono,39 V. Onuchin,12 A. Oskarsson,20 L. Osterman,20 I. Otterlund,20 K. Oyama,7, 38

L. Paffrath,4, ∗ A.P.T. Palounek,19 V.S. Pantuev,34 V. Papavassiliou,26 S.F. Pate,26

T. Peitzmann,22 A.N. Petridis,13 C. Pinkenburg,4, 33 R.P. Pisani,4 P. Pitukhin,12 F. Plasil,27

M. Pollack,34, 36 K. Pope,36 M.L. Purschke,4 I. Ravinovich,42 K.F. Read,27, 36 K. Reygers,22

V. Riabov,28, 31 Y. Riabov,28 M. Rosati,13 A.A. Rose,40 S.S. Ryu,43 N. Saito,29, 30

A. Sakaguchi,11 T. Sakaguchi,7, 41 H. Sako,39 T. Sakuma,29, 37 V. Samsonov,28

T.C. Sangster,18 R. Santo,22 H.D. Sato,17, 29 S. Sato,39 S. Sawada,14 B.R. Schlei,19

Y. Schutz,35 V. Semenov,12 R. Seto,5 T.K. Shea,4 I. Shein,12 T.-A. Shibata,29, 37

K. Shigaki,14 T. Shiina,19 Y.H. Shin,43 I.G. Sibiriak,16 D. Silvermyr,20 K.S. Sim,15

J. Simon-Gillo,19 C.P. Singh,2 V. Singh,2 M. Sivertz,4 A. Soldatov,12 R.A. Soltz,18

S. Sorensen,27, 36 P.W. Stankus,27 N. Starinsky,21 P. Steinberg,8 E. Stenlund,20

A. Ster,44 S.P. Stoll,4 M. Sugioka,29, 37 T. Sugitate,11 J.P. Sullivan,19 Y. Sumi,11

Z. Sun,6 M. Suzuki,39 E.M. Takagui,32 A. Taketani,29 M. Tamai,41 K.H. Tanaka,14

Y. Tanaka,24 E. Taniguchi,29, 37 M.J. Tannenbaum,4 J. Thomas,34 J.H. Thomas,18

T.L. Thomas,25 W. Tian,6, 36 J. Tojo,17, 29 H. Torii,17, 29 R.S. Towell,19 I. Tserruya,42

H. Tsuruoka,39 A.A. Tsvetkov,16 S.K. Tuli,2 H. Tydesjo,20 N. Tyurin,12 T. Ushiroda,24

H.W. van Hecke,19 C. Velissaris,26 J. Velkovska,34 M. Velkovsky,34 A.A. Vinogradov,16

M.A. Volkov,16 A. Vorobyov,28 E. Vznuzdaev,28 H. Wang,5 Y. Watanabe,29, 30

S.N. White,4 C. Witzig,4 F.K. Wohn,13 C.L. Woody,4 W. Xie,5, 42 K. Yagi,39

S. Yokkaichi,29 G.R. Young,27 I.E. Yushmanov,16 W.A. Zajc,8, † Z. Zhang,34 and S. Zhou6

(PHENIX Collaboration)

1Institute of Physics, Academia Sinica, Taipei 11529, Taiwan

2Department of Physics, Banaras Hindu University, Varanasi 221005, India

3Bhabha Atomic Research Centre, Bombay 400 085, India

4Brookhaven National Laboratory, Upton, NY 11973-5000, USA

5University of California - Riverside, Riverside, CA 92521, USA

6China Institute of Atomic Energy (CIAE), Beijing, Peoples Republic of China

7Center for Nuclear Study, Graduate School of Science, University

of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan

8Columbia University, New York, NY 10027 and

Nevis Laboratories, Irvington, NY 10533, USA

9Florida State University, Tallahassee, FL 32306, USA

10Georgia State University, Atlanta, GA 30303, USA

11Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan

12Institute for High Energy Physics (IHEP), Protvino, Russia

13Iowa State University, Ames, IA 50011, USA

14KEK, High Energy Accelerator Research

Organization, Tsukuba-shi, Ibaraki-ken 305-0801, Japan

15Korea University, Seoul, 136-701, Korea

16Russian Research Center “Kurchatov Institute”, Moscow, Russia

17Kyoto University, Kyoto 606, Japan

18Lawrence Livermore National Laboratory, Livermore, CA 94550, USA

19Los Alamos National Laboratory, Los Alamos, NM 87545, USA

20Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden

21McGill University, Montreal, Quebec H3A 2T8, Canada

22Institut fuer Kernphysik, University of Muenster, D-48149 Muenster, Germany

23Myongji University, Yongin, Kyonggido 449-728, Korea

24Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan

25University of New Mexico, Albuquerque, NM, USA

26New Mexico State University, Las Cruces, NM 88003, USA

27Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

28PNPI, Petersburg Nuclear Physics Institute, Gatchina, Russia

29RIKEN (The Institute of Physical and Chemical

Research), Wako, Saitama 351-0198, JAPAN

30RIKEN BNL Research Center, Brookhaven

National Laboratory, Upton, NY 11973-5000, USA

31St. Petersburg State Technical University, St. Petersburg, Russia

32Universidade de Sao Paulo, Instituto de Fisica,

Caixa Postal 66318, Sao Paulo CEP05315-970, Brazil

33Chemistry Department, State University of New

York - Stony Brook, Stony Brook, NY 11794, USA

34Department of Physics and Astronomy, State University

of New York - Stony Brook, Stony Brook, NY 11794, USA

35SUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3,

Universite de Nantes) BP 20722 - 44307, Nantes, France

36University of Tennessee, Knoxville, TN 37996, USA

37Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan

38University of Tokyo, Tokyo, Japan

39Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan

40Vanderbilt University, Nashville, TN 37235, USA

41Waseda University, Advanced Research Institute for Science and

Engineering, 17 Kikui-cho, Shinjuku-ku, Tokyo 162-0044, Japan

42Weizmann Institute, Rehovot 76100, Israel

43Yonsei University, IPAP, Seoul 120-749, Korea

44 KFKI Research Institute for Particle and Nuclear Physics (RMKI), Budapest, Hungary

(Dated: February 8, 2008)

Abstract

Transverse momentum spectra and yields of hadrons are measured by the PHENIX collaboration

in Au + Au collisions at√

sNN = 130 GeV at the Relativistic Heavy Ion Collider (RHIC). The time-

of-flight resolution allows identification of pions to transverse momenta of 2 GeV/c and protons

and antiprotons to 4 GeV/c. The yield of pions rises approximately linearly with the number

of nucleons participating in the collision, while the number of kaons, protons, and antiprotons

increases more rapidly. The shape of the momentum distribution changes between peripheral and

central collisions. Simultaneous analysis of all the pT spectra indicates radial collective expansion,

consistent with predictions of hydrodynamic models. Hydrodynamic analysis of the spectra shows

that the expansion velocity increases with collision centrality and collision energy. This expansion

boosts the particle momenta, causing the yield from soft processes to exceed that for hard to large

transverse momentum, perhaps as large as 3 GeV/c.

∗Deceased†PHENIX Spokesperson:zajc@nevis.columbia.edu

I. INTRODUCTION

Heavy ion reactions at ultrarelativistic energies provide information on strongly inter-

acting matter under extreme conditions. Lattice QCD and phenomenological predictions

indicate that at high enough energy density a deconfined state of quarks and gluons, the

quark-gluon-plasma, is formed. It is expected that conditions in ultrarelativistic heavy ion

reactions may produce this new state of matter, the study of which is the major goal of the

experiments at the Relativistic Heavy Ion Collider (RHIC).

The high energy density state thus created will cool down and expand, undergoing a phase

transition to “ordinary” hadronic matter. While the tools of choice to study the earliest

phase of the reactions, and thereby the new state, are probes that do not interact via the

strong force, such as photons, electrons, or muons, the global properties and dynamics of

later stages in the system are best studied via hadronic observables. Hadron momentum

spectra in proton-proton reactions are often separated into two parts, a soft part at low

transverse momentum (pT ), where the shape is roughly exponential in transverse mass mT =√

p2T + m2

0, and a high pT region where the shape more closely resembles a power law. Soft

production (low pT ) is attributed to fragmentation of a string [1, 2] between components of

the struck nucleons, while hard (high pT ) hadrons are expected to originate predominantly

from fragmentation of hard-scattered partons. The transition between these two regimes is

not sharply defined, but is commonly believed to be near pT ≈ 2 GeV/c [3].

In proton-nucleus (p+A) scattering, these two regimes depend on the colliding system

size in different ways. The soft production depends on the number of nucleons struck, or

participating in the collision (Npart). The number of hard scatterings should increase pro-

portionally to the number of binary nucleon-nucleon encounters (Ncoll) since these processes

have a small elementary cross section and may be considered as incoherent. Hard scattering

also produces color strings which fragment and produce some low pT particles, though these

are much fewer in number than those from the much more frequent soft scatterings. In p+A

these Npart and Ncoll are connected by a very simple relation, namely Npart = Ncoll + 1.

In nucleus-nucleus collisions, the number of participant nucleons does not scale simply

with A, so it is more useful to study scaling with Ncoll or Npart. Collisions are sorted

according to centrality, allowing control of the geometry and determination of Ncoll or Npart.

In heavy ion collisions, one expects secondary collisions of particles (rescattering) to

take place, especially among particles with low and intermediate transverse momentum.

Rescattering may occur among partons early in the collision, and also among hadrons later in

the collision. Both kinds of rescattering can lead to collective behavior among the particles,

and the presence of elliptic flow ([4, 5, 6, 7, 8, 9]) indicates that partonic rescattering is

important at RHIC. In the extreme, rescattering can lead to thermalization. Rescattering

has observable consequences on the final hadron momentum spectra, causing them to be

broadened as shown in this paper. This relates to some of the key questions regarding the

evolution of the collision: Are the size and lifetime sufficient to attain local equilibrium? Are

the momentum distributions thermal, and if so, what are the chemical and kinetic freeze-

out temperatures? Can expansion be described by hydrodynamic models? Momentum

distributions of hadrons as a function of centrality provide a means to investigate these

questions and permit extraction of thermodynamic quantities which govern the predicted

phase transition.

This paper reports semi-inclusive momentum spectra and yields of π, K, and p from Au-

Au collisions at√

sNN = 130 GeV. The data are measured and analyzed by the PHENIX

Collaboration in the first year of the physics program at RHIC (Run-1).

The paper is organized as follows. In Section II the PHENIX detectors used in the analysis

are described. The data reduction techniques using the Time-of-Flight and Drift Chamber

detectors, along with the corrections applied to the spectra, are described in Section III.

Functions that describe the shape of the spectra are used to extrapolate the unmeasured por-

tion in order to determine the total average momentum and particle yield for each particle.

The overall systematic uncertainties in the spectra are discussed. The resulting minimum

bias and centrality-selected particle spectra are presented in Section IV. In Section V a de-

scription of the particle production within a hydrodynamic picture is investigated. For each

centrality selection, a hydrodynamic parameterization of the mT distribution is fit simul-

taneously to the spectra of different species. The data are compared to full hydrodynamic

calculations. The transition region in pT between hard (perturbative QCD) and soft (hy-

drodynamic behavior) physics is investigated by comparison of extrapolated soft spectra to

the data. Finally, we study the dependence of the particle yields on the number of nucleons

participating in the collision.

II. EXPERIMENT

The PHENIX [10, 11] experiment at RHIC identifies hadrons over a large momentum

range, by the addition of excellent time-of-flight capability to the detector suite optimized

for photons, electrons, and muons. PHENIX has four spectrometer arms, two that are

positioned about midrapidity (the central arms) and two at more forward rapidities (the

Muon Arms). A cross-sectional view of the PHENIX detector, transverse to the beamline

is shown in Figure 1. Within the two central arm spectrometers, the detectors that were

instrumented and operational during the√

sNN = 130 GeV run (Run-1) are shown. The

detector systems in PHENIX are discussed in detail elsewhere [12]. The detector systems

used for the measurements reported in this paper are described in detail in the following

sections.

A. CENTRAL ARM DETECTORS

The central arm spectrometers use a central magnet that produces an approximately

axially symmetric field that focuses charged particles into the detector acceptance. The two

central arms are labeled as East and West Arms. The East Arm contains the following

subsystems used in this analysis: drift chamber (DC), pad chamber (PC), and a Time-of-

Flight (TOF) wall. The PHENIX hadron acceptance using the TOF system in the East

Arm is illustrated in Figure 2 where the transverse momentum is plotted as a function of

the particle rapidity (the phase space) within the central arm acceptance subtending the

polar angle θ from 70 to 110 degrees for pions, kaons, and protons. The vertical lines are

the equivalent pseudorapidity edges, corresponding to |η| < 0.35. More details are discussed

elsewhere [13].

1. TRACKING CHAMBERS

The charged particle tracking chambers include three layers of pad chambers and two drift

chambers. The chambers are designed to operate in a high particle multiplicity environment.

The drift chambers are the first tracking detectors that charged particles encounter as

they travel from the collision vertex through the central arms. Each is 1.8 m in width in the

beam direction, subtends 90-degrees in azimuthal angle φ, centered at a radius RDC = 2.2 m,

West BeamView

PHENIX Detector - First Year Physics Run

Installed

ActivePbSc PbSc

PbSc PbSc

PbSc PbGl

PC1 PC1

CentralMagnet TEC

RICH RICH

FIG. 1: A cross-sectional view of the PHENIX detector, transverse to the beamline. Within the

two central arm spectrometers the detectors that were instrumented and operational during the

√sNN = 130 GeV run are shown.

and is filled with a 50-50 Argon-Ethane gas mixture. It consists of 40 planes of sense wires

arranged in 80 drift cells placed cylindrically symmetric about the beamline. The wire planes

are placed in an X-U-V configuration in the following order (moving outward radially): 12

X planes (X1), 4 U planes (U1), 4 V planes (V1), 12 X planes (X2), 4 U planes (U2), and

4 V planes (V2). The U and V planes are tilted by a small ±5o stereo angle to allow for

full three-dimensional track reconstruction. The field wire design is such that the electron

drift to each sense wire is only from one side, thus removing most left-right ambiguities

everywhere except within 2 mm of the sense wire. The wires are divided electrically in the

middle at the beamline center. The occupancy for a central RHIC Au+Au collision is about

0 < 110θ < 070 (

y-0.5 -0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3 0.4 0.50

FIG. 2: The central arm spectrometer acceptance in rapidity and transverse momentum for pions

(top), kaons (middle), and protons (bottom).

two hits per wire.

At the drift chamber location, the field of the central magnet is nearly zero, so the DC

determines (nearly) straight-line track segments in the r-φ plane. Each track segment is in-

tersected with a circle at RDC , where it is characterized by two angles: the angular deflection

in the main bend plane, and the azimuthal position in φ. A combinatorial Hough transform

technique (CHT) is used to identify track segments by searching for location maxima in this

angular space/citehough. The DCs are calibrated with respect to the event collision time

measurement (see Section IIB). With this calibration, the single-wire resolution in the r-φ

plane is 160 µm. The single-track wire efficiency is 99% and the two-track resolution is

better than 1.5 mm.

The drift chambers are used to measure the momentum of charged particles and the

direction vector for charged particles traversing the spectrometer. The angular deflection

is inversely proportional to the component of momentum in the bend plane only. Both the

bend angle and the measured track points are used in the momentum reconstruction and

track model, which uses a look-up table of the measured central magnet field grid. For this

data set, the drift chamber momentum resolution is σp/p = 0.6% ⊕ 3.6%p, where the first

term is multiple scattering up to the drift chambers and the second is the angular resolution

of the detector.

In Run-1, there were three pad chambers in PHENIX. Each pad chamber measures a

three-dimensional space point of a charged track. The pad chambers are pixel-based detec-

tors with effective readout sizes of 8.45 mm along the beamline by 8.40 mm in the plane

transverse to the beamline. The first pad chamber layer (PC1) is fixed to the outer edge

radially of each drift chamber at a radial distance of 2.49 m, while the third layer (PC3)

is positioned at 4.98 m from the beamline. Both arms include PC1 chambers, while only

the East Arm is instrumented with PC3. The second layer (PC2) is located at an inner

inscribed radius of 4.19 m in the West Arm and was not installed for Run-1.

The position resolution of PC1 is 1.6 mm along the beam axis and 2.3 mm in the plane

transverse to the beam axis. The position resolutions of PC3 are 3.2 mm and 4.8 mm,

respectively. The PC3 is used to reject background from albedo and non-vertex decay

particles; however, only the PC1 is used for the results presented here. The PC1 is used

in the global track reconstruction with the measured vertex position using the beamline

detectors (see Section IIB) to determine the polar angle of each charged track. Both PC1

and the beamline detectors provide z-coordinate information with a 1.89 mm resolution.

2. TIME OF FLIGHT

The Time-of-Flight detector (TOF) serves as the primary particle identification device

for charged hadrons by the measurement of their arrival time at the TOF wall 5.1 m from

the collision vertex. The TOF wall spans 30 in azimuth in the East Arm. It consists of 10

panels of 96 scintillator slats each with an intrinsic timing resolution better than 100 ps. Each

slat is oriented along the r-φ direction and provides timing as well as beam-axis position

information for each particle hit recorded. The slats are viewed by two photomultiplier

tubes, attached to either end of the scintillator. A ±2σ π/K separation at momenta up to

2.0 GeV/c, and a ±2σ (π+K)/proton separation up to 4.0 GeV/c can be achieved.

For each particle, the time, energy loss in the scintillator, and geometrical position are

determined. The total time offset is calibrated slat by slat. A particle hit in the scintillator

is defined by a measured pulse height which is also used to correct the time recorded at each

end of the slat (slewing correction). After calibration, the average of the times at either end

of the slat is the measured time for a particle. The azimuthal position is proportional to the

time difference across the slat and the known velocity of light propagation in the scintillator

(for Bicron BC404, this is 14 cm/ns). The slat position along the beamline determines

the longitudinal coordinate position of the particle. The total time of flight is measured

relative to the Beam-Beam counter initial time (see Section IIB), the measured time in the

Time-of-Flight detector, and a global time offset from the RHIC clock. Positive pions in the

momentum range 1.4 < pT < 1.8 GeV/c are used to determine the TOF resolution. The

timing calibration in this analysis results in a resolution of σ = 115 ps.1

Particle identification for charged hadrons is performed by combining the information

from the tracking system with the timing information from the BBC and the TOF. Tracks

at 1 GeV/c in momentum point to the TOF with a projected resolution σproj of 5 mrad in

azimuthal angle and 2 cm along the beam axis. Tracks that point to the TOF with less

than 2.0 σproj were selected. Figure 3 shows the resulting time-of-flight as a function of the

reciprocal momentum in minimum-bias Au+Au collisions.

1 Ultimately, 96 ps results after further calibration, as reported in [12].

FIG. 3: Scaled Time-of-Flight versus reciprocal momentum in minimum-bias Au+Au collisions at

√sNN = 130 GeV. The distribution demonstrates the particle identification capability using the

TOF for the Run-1 data taking period.

B. BEAMLINE DETECTORS

The beamline detectors determine the collision vertex position along the beam direction,

and the trigger and timing information for each event. These detectors include the Zero

Degree Calorimeters (ZDCs), the Beam-Beam Counters (BBC), and the Multiplicity Vertex

Detector (MVD) and are positioned in PHENIX as shown in Figure 4.

The Zero Degree Calorimeters are small transverse area hadron calorimeters that are

installed at each of the four RHIC experiments. They measure the fraction of the energy

South Side View North

MuID MuID

Central Magnet

North M

uon Mag

ZDC NorthZDC South

Installed Active

PHENIX Detector - First Year Physics Run

FIG. 4: A side view of the PHENIX detector, parallel to the beamline. The beamline detec-

tors determine the collision vertex position along the beam direction, and the trigger and timing

information for each event.

deposited by spectator neutrons from the collisions and serve as an event trigger for each

RHIC experiment. The ZDCs measure the unbound neutrons in small forward cones (θ <2

mrad) around each beam axis. Each ZDC is positioned 18 m up and downstream from the

interaction point along the beam axis. A single ZDC consists of 3 modules each with a depth

of 2 hadronic interaction lengths and read out by a single PMT. Both time and amplitude

are digitized for each of the 3 PMTs as well as an analog sum of the PMTs for each ZDC.

There are two Beam-Beam counters each positioned 1.4 m from the interaction point, just

behind the central magnet poles along the beam axis (see Figure 4). The BBC consists of

two identical sets of counters installed on both sides of the interaction point along the beam.

Each counter consists of 64 Cherenkov telescopes, arranged radially about the collision axis

and situated north and south of the MVD. The BBCs measure the fast secondary particles

produced in each collision at forward angles, with 3.0 ≤ η ≤ 3.9, and full azimuthal coverage.

For both the ZDC and the BBC, the time and vertex position are determined using the

measured time difference between the north and the south detectors and the known distance

between the two detectors. The start time (T0) and the vertex position along the beam axis

(Zvertex) are calculated as T0 = (T1 + T2)/2 and Zvertex = (T1 − T2)/2c, where T1 and T2 are

the average timing of particles in each counter and c is the speed of light. With an intrinsic

timing resolution of 150 ps, the ZDC vertex is measured to within 3 cm. In Run-1, the BBC

timing resolution of 70 ps results in a vertex position resolution of 1.5 cm.

Event centrality is determined using a correlation measurement between neutral energy

deposited in the ZDCs and fast particles recorded in the BBCs as shown in Figure 5. The

spectator nucleons are unaffected by the interaction and travel at their initial momentum

from each respective ion. The number of neutrons measured by the ZDC is proportional to

the number of spectators, while the BBC signal increases with the number of participants.

III. DATA REDUCTION AND ANALYSIS

A. DATA REDUCTION

The PHENIX Level-1 trigger selected events with hits coincident in both the ZDC and

BBC detectors, and in time with the RHIC clock. A total of 5M events were recorded

sNN = 130 GeV in the ZDCs [11]. The collision position along the beam direction

was required to be within ± 30 cm of the center of PHENIX, using the collision vertex

reconstructed by the BBC.

The trigger on both BBC and both ZDC counters includes 92± 4% of the total inelastic

cross section (6.8± 0.4 barns). A Monte Carlo Glauber model [15] is used with a simulation

of the BBC and ZDC responses to determine the number of nucleons participating in the

collisions for the minimum bias events. The Woods-Saxon parameters determined from

electron scattering experiments are: radius = 6.38±0.06 fm, diffusivity = 0.54±0.01 fm [16],

and the nucleon-nucleon inelastic cross-section, σinelN+N = 40±3 mb. An additional systematic

uncertainty enters the radius parameter since the radial distribution of neutrons in large

nuclei should be larger than for protons and is not well determined [17].

The centrality selections used in this paper are 0-5%, 5-15%, 15-30%, 30-60%, and 60-92%

of the total geometrical cross section, where 0-5% corresponds to the most central collisions.

maxBBC/QBBCQ

0 0.2 0.4 0.6 0.8 1

1BBC vs ZDC analog response

10-15%

15-20%

Number of tracks0 20 40 60 80 100 120 140 160 180

0 200 400 600η=0|/dηchdN

Minimum bias multiplicity distributionat mid-rapidity

FIG. 5: The event centrality (upper plot) is determined using a correlation measurement of the

fraction of neutron energy recorded in the ZDCs (vertical scale) and the fractional charge measured

in the BBCs (horizontal scale). The equivalent track multiplicity in each centrality selection is

shown in the lower plot.

Only tracks which are reconstructed in all three dimensions are included in the spectra.

These tracks are then matched within 2σproj to the measured positions in the TOF detector.

For each TOF hit, the time, position, and energy loss are measured in the TOF detector. The

widths of residual distance distributions between projected tracks and TOF hit positions,

σproj, increase at lower momentum due to multiple scattering. Therefore, a momentum-

dependent hit association criterion was defined.

Finally, a requirement on energy loss in the TOF is applied to each track to exclude

false hits by requiring the energy deposit of at least minimum ionizing particle energy. A β-

dependent energy loss cut whose form is a parameterization of the Bethe-Bloch formula[18]

is used, where

dE/dx ≈ β−5/3 (1)

and β = L/ct, where L is the pathlength of the particle’s trajectory from the BBC vertex

to the TOF detector, t is the particle’s time-of-flight, and c is the speed of light. The

approximate Bethe-Bloch formula is scaled by a factor to fall below the data and thereby

serve as a cut. The resulting equation is ∆E = Aβ−5/3 where A is a scaling factor equal

to 1.6 MeV. The energy loss cut reduces low momentum background under the kaon and

proton mass peaks. The fraction of tracks excluded after the energy loss cut is less than

The measured momentum (p), pathlength (L), and time of flight (t) in the spectrometer

are used to calculate the particle mass, which is used for particle identification:

m2 =p2

The width of the peaks in the mass-squared distribution depend on both the momentum

and time-of-flight resolutions. An analytic form for the width of m2 as a function of momen-

tum resolution σp and time of flight resolution is determined using Equation 2. The error in

the particle’s pathlength L results in an effective time width that is included with the TOF

resolution, σT ,

σ2m2 = 4m4σp

+ 4p4 1

The momentum resolution of the drift chambers is expressed in the following form

σ2p =

C2p2)2

C1 =δφms

K1, (5)

C2 =δφα

K1, (6)

where C1 and C2 are the multiple scattering and angular resolution terms, respectively. The

units of δφms are mrad GeV/c. The constant K1 is the momentum kick on the particle from

the magnetic field and is equal to 87.3 mrad GeV/c. The constant C1 is the width in φ due

to the multiple scattering (ms) of a charged particle with materials of the spectrometer up

to the drift chambers. The C2 term is the angular resolution of the bend angle (α), which is

the angular deflection in φ of the track segment relative to the radius to the collision vertex.

Equation 4 is used in Equation 3 with β = p/√

p2 + m20, where m0 is the mass centroid

of the particle’s mass-squared distribution. The mass centroid is close to the rest mass of

the particle; however due to residual misalignments and timing calibration, the centroid of

the distribution is a fit parameter in order to avoid cutting into the distribution. The m2

width for each particle is written as follows:

σ2m2 = (7)

C21 · 4m4(1 +

p2 ) + C22 · 4m4

0p2 + C2

3 · (4p2(m20 + p2))

where the coefficient C3 is related to the combined TOF,

C3 =σT c

L, (8)

and pathlength contributions to the time width, σT in Equation 8. From the measured

drift chamber momentum resolution, C1 = 0.006 and C2 = 0.036 c/GeV. While the TOF

resolution is 115±5 ps, the pathlength uncertainty introduces a width of ≈ 20-40 ps, so 145

ps is used for σT in C3.

The pions, kaons, and protons are identified using the measured peak centroids of the m2

distribution and selecting 2σ bands; shown as shaded regions in Figure 6 for two different

momentum slices. The 2σ bands for pions and kaons do not overlap up to pT =2 GeV/c.

The protons are identified up to pT = 4 GeV/c. By studying variations in the m2 centroid

and width before the particle identification cut is applied, the uncertainty in the particle

identification is estimated to be 5% for all particles.

Kaons are depleted by decays in flight and geometrical acceptance. For the low mo-

mentum protons, energy loss and geometrical acceptance cause a drop in the raw yield for

pT < 0.5 GeV/c, as seen in Figure 2.

0.7 < p < 0.8 GeV/c

)4/c2 (GeV2m-0.2 0 0.2 0.4 0.6 0.8 1 1.2

103 1.3 < p < 1.5 GeV/c

FIG. 6: The mass-squared distributions of positive pions, kaons, and protons for two different

momentum slices. The momentum slice 0.7 < p < 0.8 GeV/c is the upper panel and 1.3 < p < 1.5

GeV/c is the lower panel. The shaded regions correspond to the 2σ particle identification bands

based on the calculated mass-squared width, the measured mass-squared centroids, and the known

detector resolutions.

The remaining background contribution was determined by reflecting the track about the

midpoint of PHENIX along the beamline and repeating the association and PID cuts used

in the TOF detector. This random background was evaluated separately for each particle

type. The background contribution is ≈ 30% for the kaon spectra at 0.2 < pT < 0.4 GeV/c

and defines the low pT limit in the spectra. The background is < 5% in all other cases,

and negligible above 0.8 GeV/c in the measured momentum range in this analysis. The

background was not subtracted but is instead treated as a systematic uncertainty. This

uncertainty is 2, 5, and 3% for pions, kaons, and protons, respectively, at pT < 0.6 GeV/c

and is negligible at higher momenta.

B. ANALYSIS

The raw spectra include inefficiencies from detector acceptance, resolution, particle decays

in flight and track reconstruction. The baseline efficiencies are determined by simulating

and reconstructing single hadrons. Multiplicity dependent effects are then evaluated by

embedding simulated single hadrons into real events and calculating the degradation of the

reconstruction efficiency.

1. CORRECTIONS: ACCEPTANCE, DECAYS IN FLIGHT, AND DETECTOR RE-

SPONSE

The corrections for the finite detector aperture, pion and kaon decays in flight, and the

detector response are determined using single particles in the the GEANT [19] simulation

of the detector. All details of each detector are modeled, including dead channels in the

drift chambers, pad chambers, and Time-of-Flight detector. All physics processes are au-

tomatically taken into account, resulting in corrections for multiple scattering, anti-proton

annihilation, pion and kaon decays in flight, finite geometrical acceptance of the detector,

and momentum resolution, which affects the spectral shape above 2.5 GeV/c.

The drift chamber simulated response is tuned to describe the response of the real drift

chambers on the single-wire level. This is done using a simple geometrical model of the drift

chamber and the straight-line trajectories of particles from the zero-field data. This simple

model of the drift cell in the drift chamber is sufficient to describe the observed drift distance

distribution, the pulse width, the single wire efficiency, and the detector resolution. The TOF

response is simulated by smearing the true time of flight using a Gaussian distribution with

a width as measured in the data.

Figure 7 shows the momentum dependence of the residual distance between projected

tracks and TOF hits for the real (solid line) and simulated (dashed) events. These residuals

are parameterized in the azimuthal angle φ and the beamline direction z, separately for data

and simulation. For each case, tracks that fall outside 2σ of the parameterized width are

rejected, thus allowing use of the Monte Carlo to evaluate the correction for the 2σ match

requirement for real tracks.

p (GeV/c)0 0.5 1 1.5 2

Monte Carlo

p (GeV/c)0 0.5 1 1.5 2

FIG. 7: Comparison of the momentum-dependent residuals of DC tracks matched to TOF hits in

azimuthal angle φ (left) and z (right) between data (solid) and simulation (dashed).

A fiducial cut is made in both the simulation and in the data to ensure the same fiducial

volume. The systematic uncertainty in the acceptance correction is approximately 5%.

The simulated distributions are generated uniformly in pT , φ, and y. For each hadron,

sufficient Monte Carlo events are generated to obtain the correction factor for every measured

pT bin. The statistical errors from the correction factors were smaller than those in the data

and both are added in quadrature.

The distribution of the number of particles generated in each pT slice, dN/dpT , is the

“ideal” input distribution without detector and reconstruction effects. This distribution is

normalized to 2π and 1 unit of rapidity. After detector response and track reconstruction,

the output distribution is the number of particles found in each pT slice. The final correc-

tions are determined after an iterative weighting procedure. First, the flat input and output

distributions are weighted by exponential functions for all particles using an inverse slope of

300 MeV. The ratio of input to output distributions is determined as a function of momen-

tum. In each pT slice, the corresponding ratio is applied to the data. The corrected data are

next fitted with exponentials for kaons and protons (see Equation 11), and a power-law for

the pions (see Equation 9). The original flat input and output distributions are weighted

by these resulting functions. The procedure is repeated until the functions remain constant

in their parameters. The weighted input and output distributions are divided to produce

acceptance correction factors. The corrections are larger for kaons due to the decays in

flight. The statistical error in determination of the correction factor is added in quadrature

to the statistical error in the data.

2. HIGH TRACK-DENSITY EFFICIENCY CORRECTION

A final multiplicity dependent correction is determined using simulated single-particles

embedded into real events. This correction depends on both the quality of the track recon-

struction in a high multiplicity environment and the type of particle measured.

Depending on the centrality of the event, the correction factor is determined for each

particle in the raw transverse momentum distribution and is applied as a weight. The final

efficiency corrections are shown in Figure 8, where the correction for pions is shown as

solid circles and for (anti)protons as open circles. The horizontal axis ranges from the most

central to the most peripheral events in increments of 5%. The systematic uncertainty in

the multiplicity efficiency correction is 9%.

The difference between pions (solid) and (anti)protons (open) is due to the different TOF

efficiencies for each particle (protons are slower than pions). In a small fraction of cases two

particles may hit the same TOF slat at different times, and the slower particle is assigned

an incorrect time. The particle will then fall outside the particle identification cuts. This

effect depends on the type of particle.

For each particle, two curves are shown, representing the DC tracking inefficiency for two

types of tracks: fully reconstructed and partially reconstructed tracks. Fully reconstructed

tracks include X1 and X2 sections. In a high track-density environment, tracks may be

partially reconstructed or hits may be incorrectly associated. There are two cases when

this incorrect hit association occurs. In the first case, the direction vector in the azimuth

prevents the track from pointing properly to the PC1 detector, and the correct hit cannot

be associated. In the second case, the track is reconstructed properly, but there are two

possible PC1 points. If no UV hits are found, then the wrong PC1 point can be associated

to the track and the track’s beamline coordinate is mis-reconstructed. In both of these cases,

the track fails the matching criteria in the TOF detector and is lost.

Centrality (%)0 10 20 30 40 50 60 70 80 90 100

Fully reconstructed tracks

Partially reconstructed tracks

FIG. 8: The multiplicity dependent efficiency correction for pions (solid) and (anti)protons (open)

for two types of tracks. The upper set of points correspond to fully reconstructed tracks in the

drift chambers; while the lower set of points correspond to partially reconstructed tracks in the

drift chambers.

3. DETERMINING THE YIELD AND MEAN pT

The dN/dy and 〈pT 〉 are determined using the data in the measured region and an

extrapolation to the unmeasured region after integrating a functional form fit to the data.

A function describing the spectral shape is fit to the data, with varying pT ranges to control

systematic uncertainties in the fit parameters. The fitted shape is extrapolated, integrated

over the unmeasured range, and then combined with the measured data to get the full yield.

Two different functions are used to estimate upper and lower bounds for each spectrum. The

average between the upper and lower bounds is used for dN/dy and 〈pT 〉. The statistical error

is determined from the data, and the systematic uncertainty is taken as 1/2 the difference

between the upper and lower bounds.

For pions, a power-law in pT (Equation 9) and an exponential in mT (=√

p2T + m2

(Equation 10) are fit to the data. For kaons and (anti)protons, two exponentials, one in pT

(Equation 11) and the other in mT are used. The pT exponential provides an upper limit

for the extrapolated yield, which is most important for the (anti)protons. The power-law

function has three parameters labeled A, p0, and n in Equation 9. The exponentials have

two parameters, A and T .d2N

2πpT dpT dy= A

p0 + pT

2πmT dmT dy= Ae−mT /T (10)

2πpT dpT dy= Ae−pT /T (11)

C. SYSTEMATIC UNCERTAINTIES

In Table I, the sources of systematic uncertainties in both 〈pT 〉 and dN/dy are tabulated.

The sources of uncertainty include the extrapolation in pT , the background, and the Monte

Carlo corrections and cuts. The uncertainty in the Monte Carlo corrections is 11% and

includes: the multiplicity efficiency correction of 9%, the particle identification cut of 5%,

and the fiducial cuts of 5%. The uncertainties in the correction functions are added in

quadrature to the statistical error in the data. Background is only relevant for pT < 0.6

GeV/c in the spectra.

The total systematic uncertainty in the 〈pT 〉 depends on the extrapolation and back-

ground uncertainties; the uncertainties are 7%, 10%, and 8% for pions, kaons, and protons,

respectively. The overall uncertainty on dN/dy includes the uncertainties on 〈pT 〉 in addi-

tion to the uncertainties from the corrections and cuts; the uncertainties are 13%, 15%, and

14% for pions, kaons, and protons, respectively [20].

The hadron yields and 〈pT 〉 values include an additional uncertainty arising from the

fitting function used for extrapolation to the unmeasured region at low and high pT . The

magnitude of the extrapolation is 30 ± 6% of the spectrum for pions, 40 ± 8% for kaons,

and 25± 7.5% for protons [20]. The systematic uncertainty quoted here is taken as 1/2 the

difference between the results from the two different functional forms.

TABLE I: The sources of systematic uncertainties in 〈pT 〉 and dN/dy.

π (%) K (%) (anti)p (%)

Extrapolation 6 8 7.5

Background (pT < 0.6 GeV/c) 2 5 3

〈pT 〉 total 7 10 8

Corrections and cuts 11 11 11

dN/dy total 13 15 14

The momentum scale is known to better than 2%, and the momentum resolution affects

the spectra shape, primarily for protons, above 2.5 GeV/c. The momentum resolution is

corrected by the Monte Carlo. As other sources of uncertainty on the number of particles

at any given momentum are much larger, momentum resolution effects are neglected in

determining the overall systematic uncertainty from the data reduction.

IV. RESULTS

A. TRANSVERSE MOMENTUM DISTRIBUTIONS

The invariant yields as a function of pT for identified hadrons are shown in Figure 9, while

Figure 10 provides the centrality dependence of the spectra. The spectra are tabulated in

Appendix B. The π±, K±, p, and p invariant yields for the most central, mid-central,

and the most peripheral collisions, were reported previously [21]. Pion and (anti-)proton

invariant yields are comparable for pT >1 GeV in the most central collisions.

As can be seen already from Figure 10 all the spectra seem to be exponential; however,

upon closer inspection, small deviations from an exponential form are apparent for the more

peripheral collisions. The spectrum in the most peripheral collisions is noticeably power-

(GeV/c)Tp

0 0.5 1 1.5 2 2.5 3 3.5

±π±K

pp and

Minimum biasAu+Au

= 130 GeVNNs

positive

(GeV/c)Tp

0 0.5 1 1.5 2 2.5 3 3.5

negative

FIG. 9: The spectra of positive particles (left) and negative (right) in minimum-bias collisions

from Au+Au collisions at√

sNN =130 GeV. The errors include both statistical and systematic

errors from the corrections.

law-like when compared to the more exponential-like spectrum in central collisions. This is

especially apparent for the pions. The effect can be seen more clearly in the ratio of the

spectra for a given particle species in two different centrality classes. Such ratios are shown

in Figure 11 for the 5% central and the most peripheral positive spectra (60-92% centrality).

The ratios for protons and antiprotons as well as for π+ have a maximum at intermediate

pT and are lower both at low and high pT . The kaon shape change is not very significant,

given the current statistics.

The change in slope at low-pT in central collisions compared to peripheral is consistent

with a more substantial hydrodynamic, pressure-driven transverse flow existing in central

collisions, since the increased boost would tend to deplete particles at the lowest pT (see

Section IVC). This is observed at lower energies at the CERN SPS [22, 23]. It is in contrast

to results obtained at the ISR [24] for p+p collisions at√

s = 63 GeV, where a shallow

0 0.5 1 1.5 2 2.510

102 +π

0 0.5 1 1.5 2 2.5

0-5%5-1515-3030-6060-92

0 0.5 1 1.5 2

1/(2 10

0 0.5 1 1.5 2

(GeV/c)Tp0 0.5 1 1.5 2 2.5 3 3.5

FIG. 10: The hadron spectra for five centralities from the most central 0-5% to the most peripheral

60-92% at√

sNN = 130 GeV. Errors include both the statistical and point-by-point error in the

corrections added in quadrature.

maximum or minimum exists at low pT (in the range 0.3 − 0.6 GeV/c).

1. FEED-DOWN CONTRIBUTION TO p AND p FROM INCLUSIVE Λ and Λ

Inclusive Λ and Λ transverse momentum distributions have been measured in the west arm

of the PHENIX spectrometer using the tracking detectors (DC, PC1) and a lead-scintillator

electromagnetic calorimeter (EMCal) [25]. The invariant mass is reconstructed from the

weak decays Λ → p + π− and Λ → p + π+.

The tracks from the tracking detectors are required to fall within 3σ of EMCal measured

space-points. The EMCal timing resolution of the daughter particles is ≈ 700 ps. Using the

DC momentum and the EMCal time-of-flight, the particle mass is calculated, and protons,

antiprotons, and pions are identified using 2σ momentum-dependent mass-squared cuts. A

0 0.5 1 1.5 20

0 0.5 1 1.5 2

(GeV/c)Tp0 0.5 1 1.5 2 2.5 3

FIG. 11: The ratio of the most central to the most peripheral yields as a function of pT for pions

(top), kaons (middle) and (anti)protons (bottom).

clean particle separation is obtained using an upper momentum cut of 0.6 GeV/c and 1.4

GeV/c for pions and protons, respectively. The momentum is determined assuming the

primary decay vertex is positioned at the event vertex and results in a momentum shift of

1-2% based on a Monte Carlo study.

Using all combinations of pions and protons, the invariant mass is determined. The

mass distribution shows a Λ peak on top of a random combinatorial background, which is

determined by combining protons and pions from different collisions with the same centrality.

A signal-to-background ratio of 1/2 is obtained after applying a decay kinematic cut on

the daughter particles. Fitting a Gaussian function to the mass distribution in the range

1.05 < mpπ < 1.20 GeV/c2, 12000 Λ and 9000 Λ are observed, with mass resolution δm/m ≈2%. The reconstructed Λ and Λ spectra are corrected for the acceptance, pion decay-in-

flight, momentum resolution, and reconstruction efficiency [25]. The systematic uncertainty

on the pT spectra is 13% from the corrections and 3% from the combinatorial background

subtraction. The feed-down contributions from heavier hyperons Σ0 and Ω are not measured

but are estimated to be < 5%.

In Figure 12, the transverse momentum spectra of inclusive protons (left) and antiprotons

(right) are shown with the inclusive Λ and Λ transverse momentum distributions. The solid

points are the (anti)proton spectra after the feed-down correction from Λ and Λ weak decays.

From here forward, the data that are presented and discussed are not corrected for this feed-

down effect; inclusive p and p yields are given. More details on the Λ and Λ measurement

are included in [25].

(GeV/c)Tp0 0.5 1 1.5 2 2.5 3 3.5

Λinclusive

direct p

inclusive p

Minimum bias Au+Au=130 GeVNNs

positive

(GeV/c)Tp0 0.5 1 1.5 2 2.5 3 3.5

Λinclusive pdirect

pinclusive

negative

FIG. 12: For minimum-bias collisions, the inclusive Λ, inclusive p, and direct p transverse momen-

tum distributions are plotted together in the left panel. The equivalent comparison for inclusive

Λ, p, and direct p transverse momentum distributions is in the right panel.

B. YIELD AND 〈pT 〉

The yield, dN/dy, and the average transverse momentum, 〈pT 〉, are determined for each

particle as described in the preceding section and have been previously published in [21].

For each centrality, the rapidity density dN/dy and average transverse momentum 〈pT 〉 are

tabulated in Tables II and III, respectively.

The Npart and Ncoll in each centrality selection are determined using a Glauber-model

calculation in [26]. The resulting values of Npart and Ncoll are also tabulated in Table II.

(See Appendix A for more detail). The errors on Npart and Ncoll include the uncertainties

in the model parameters as well as in the fraction of the total geometrical cross section

(92%±4%) seen by the interaction trigger. The error due to model uncertainties is 2% [26].

An additional 3.5% error results from time dependencies in the centrality selection over the

large data sample.

TABLE II: The dN/dy at midrapidity for hadrons produced at midrapidity in each centrality

class. The errors are statistical only. The systematic errors are 13%, 15% and 14% for pions,

kaons, and (anti)protons, respectively. The Npart and Ncoll in each centrality selection are from a

Glauber-model calculation in [26], also shown with systematic errors based on a 92±4% coverage.

0-5% 5-15% 15-30% 30-60% 60-92%

Npart 347.7 ± 10 271.3 ± 8.4 180.2 ± 6.6 78.5 ± 4.6 14.3 ± 3.3

Ncoll 1008.8 712.2 405.5 131.5 14.2

π+ 276 ± 3 216 ± 2 141 ± 1.5 57.0 ± 0.6 9.6 ± 0.2

π− 270 ± 3.5 200 ± 2.2 129 ± 1.4 53.3 ± 0.6 8.6 ± 0.2

K+ 46.7 ± 1.5 35 ± 1.3 22.2 ± 0.8 8.3 ± 0.3 0.97 ± 0.11

K− 40.5 ± 2.3 30.4 ± 1.4 15.5 ± 0.7 6.2 ± 0.3 0.98 ± 0.1

p 28.7 ± 0.9 21.6 ± 0.6 13.2 ± 0.4 5.0 ± 0.2 0.73 ± 0.06

p 20.1 ± 1.0 13.8 ± 0.6 9.2 ± 0.4 3.6 ± 0.1 0.47 ± 0.05

Pions dominate the charged particle multiplicity, but a large number of kaons and

(anti)protons are produced. The inclusive yield of antiprotons is nearly comparable to

that of protons. In the most central Au+Au collisions, the particle density at midrapidity

(dN/dy) is ≈ 20 for antiprotons and 28 for protons, not corrected for feed-down from strange

baryons.

The average transverse momenta increase with particle mass and with decreasing impact

parameter. The mean transverse momentum increases with the number of participant nucle-

ons by 20±5% for pions and protons, as shown in Figure 13. The 〈pT 〉 of particles produced

in p + p and pp collisions, extrapolated to RHIC energies, are consistent with the most pe-

ripheral pion and kaon data; however, the 〈pT 〉 of protons produced in Au+Au collisions is

TABLE III: The 〈pT 〉 in MeV/c for hadrons produced at midrapidity in each centrality class. The

errors are statistical only. The systematic uncertainties are 7%, 10%, and 8% for pions, kaons, and

(anti)protons, respectively.

0-5% 5-15% 15-30% 30-60% 60-92%

π+ 390 ± 10 380 ± 10 380 ± 20 360 ± 10 310 ± 30

π− 380 ± 20 390 ± 10 380 ± 10 370 ± 20 320 ± 20

K+ 560 ± 40 580 ± 40 570 ± 40 550 ± 40 470 ± 90

K− 570 ± 50 590 ± 40 610 ± 40 550 ± 50 460 ± 90

p 880 ± 40 870 ± 30 850 ± 30 800 ± 30 710 ± 80

p 900 ± 50 890 ± 40 840 ± 40 820 ± 40 800 ± 100

significantly higher. This dependence on the number of participant nucleons may be due to

radial expansion.

partN0 50 100 150 200 250 300 350

1 positive

p+K+π

partN0 50 100 150 200 250 300 350

1 negative

p-K-π

FIG. 13: The integrated mean pT for pions, kaons, and (anti)protons produced in the five different

classes of event centrality [21]. The error bars are statistical only. The systematic uncertainties are

7%, 10%, and 8% for pions, kaons, and (anti)protons, respectively. The open points are equivalent

average transverse momenta from pp and pp data, interpolated to√

s=130 GeV.

C. TRANSVERSE MASS DISTRIBUTIONS

Production of hadrons from a thermal source would make transverse mass the natural

variable for analysis. Therefore we extract inverse slopes from the transverse mass distribu-

tions by separately fitting a thermal distribution to each particle species. The Boltzmann

distribution is given in equation 12.

2πmT dmT dy= AmT e−mT /Teff , (12)

We use a simple exponential, however, with no powers of mT in the prefactor, as shown in

equation 10. This simplification is acceptable as the difference in the inverse slope is found

to be less than 2%. The simple mT exponential was also used in an equivalent analysis in

Reference [27]. The inverse slope, Teff , can be compared to other experiments, provided the

same momentum range of the spectrum is used for fitting.

If the system develops collective motion, particles experience a velocity boost from this

motion, resulting in an additional transverse kinetic energy component. This motivates use

of the transverse kinetic energy, i.e. transverse mass minus the particle rest mass, for plotting

data. Figure 14 shows the transverse kinetic energy distributions (i.e. transverse mass minus

the particle rest mass) for all positive particles (left) and negative particles (right). Pions

are in the top panel, kaons in the middle panel, and (anti)protons in the bottom panel, with

different symbols indicating different centrality bins. The solid lines are mT exponential

fits in the range (mT − m0) < 1 GeV for all particle species while the dashed lines are the

extrapolated fits. The pion spectra follow an exponential for 0.38 < (mT − m0) < 1.0 GeV

while the kaons and protons appear exponential over the entire measured mT range. The

same is true for the negative particles in the right panel; however, the antiprotons have more

curvature for (mT − m0) < 0.5 GeV. We extract Teff by fitting exponentials of the form

Equation 10 to the transverse mass spectra in the range (mT − m0) <1 GeV.

This range is chosen common for all particle species and minimizes contributions from

hard processes. Caution must be taken when comparing Teff values as the local slope of

the transverse mass spectra varies somewhat over mT for pions and antiprotons even within

this fit range. The resulting values of Teff for all particles and centralities are tabulated in

Table IV in units of MeV. The inverse slopes increase and then saturate for more central

collisions for all particles except antiprotons. The fact that the inverse slope is different for

0 0.5 1 1.5 210

/T)TAexp(-mFit Range

0 0.5 1 1.5 2

0-5% (x 5)5-15 (x 2)15-3030-6060-92

0 0.5 1 1.5

1/(2 10

+K0 0.5 1 1.5

(GeV)0-mTm0 0.5 1 1.5 2 2.5 3 3.5

FIG. 14: Transverse mass distributions of pions (top), kaons (middle), and (anti)protons (bottom)

in events with different centralities. Positive particle distributions are on the left and negative

particle distributions are on the right. The solid lines are mT exponential fits in the range (mT −

m0) < 1 GeV for all particle species while the dashed lines are the extrapolated fits.

mesons and baryons and for central and peripheral events is consistent with the mean pT

trends discussed above.

We compare to published inverse slopes of transverse mass distributions at midrapidity

from mT exponential fits in the region (mT − m0) < 1.2 GeV, listed in Table V. The

comparison includes NA44 [27, 28, 29, 30] and WA97 [31, 32] at the SPS at√

sNN = 17

GeV; and, at√

sNN = 23 GeV at the ISR, Alper et al. [33] and Guettler et al. [34]. These

data are chosen as they match the (mT − m0) range used in fitting our data. For pions,

the low-pT region of (mT − m0) < 0.3 GeV, populated by decay of baryonic resonances, is

systematically excluded from the fits. The effective temperatures are given in Table V with

the references noted accordingly.

TABLE IV: The resulting inverse slopes in MeV after fitting an mT exponential to the spectra in

the range mT −m0 <1 GeV in each event centrality classes. The pion resonance region is excluded

in the fits. The equivalent pT fit range for each particle is shown accordingly. The errors are

statistical only.

0-5% 5-15% 15-30% 30-60% 60-92%

π+ in 0.5 < pT < 1.05 GeV/c 216.8 ± 5.7 214.3 ± 4.6 217.4 ± 4.7 214.4 ± 5.2 176.9 ± 9.5

π− in 0.5 < pT < 1.05 GeV/c 215.8 ± 6.5 221.2 ± 5.6 225.3 ± 5.8 212.8 ± 5.7 215.8 ± 16.8

K+ in 0.45 < pT < 1.35 GeV/c 233.2 ± 10.8 243.6 ± 9.8 242.4 ± 9.2 228.7 ± 10.2 182.3 ± 19.0

K− in 0.45 < pT < 1.35 GeV/c 241.1 ± 15.8 244.5 ± 10.2 250.0 ± 12.3 224.2 ± 11.1 196.4 ± 22.3

p in 0.55 < pT < 1.85 GeV/c 310.8 ± 14.8 311.0 ± 12.3 293.8 ± 11.4 265.3 ± 10.9 200.9 ± 14.8

p in 0.55 < pT < 1.85 GeV/c 344.2 ± 25.3 344.0 ± 20.9 307.6 ± 17.1 275.1 ± 14.0 217.0 ± 28.3

Radial flow imparts a radial velocity boost on top of the thermal distribution. Heavy

particles are boosted to higher pT , depleting the cross section at lower pT and yielding a

higher inverse slope. Therefore, the observed inverse slope dependence on both centrality

and particle mass implies more radial expansion in more central collisions. At CERN SPS,

the Teff depends on both mass and system size (the number of participating nucleons in the

collision), indicating collective expansion. The Teff values at RHIC shown in Table IV are

somewhat larger.

In p-p collisions at similar√

s at the ISR, hadron spectra were analyzed in transverse

mass, mT , rather than transverse kinetic energy mT − m0 [35, 36]. To facilitate a direct

comparison, figure 15 shows the PHENIX hadron spectra, including π0 from the 10% most

central Au+Au collisions. The spectra approach one another, but do not fall upon a universal

curve, and thereby fail the usual definition of scaling.

It has been suggested that at transverse mass significantly larger than the rest mass of the

particle, thermal emission and radial flow may not be the only physics affecting the particle

spectra. If heavy ion collisions can be described as collisions of two sheets of colored glass

in which the gluon occupation number is sufficiently large to saturate, scaling of different

hadron spectra with transverse mass is also predicted [37]. For Au+Au collisions at different

impact parameters, the saturation scale differs, and some differences in the spectra may be

expected. Nevertheless, the authors observe that the level of mT scaling in our data is in

TABLE V: Inverse slope parameters (in MeV) of hadrons for p+p, p+nucleus, and central S+S,

S+Pb, and Pb+Pb colliding systems at CERN energies. Pb+Pb is at√

sNN = 17 GeV, and the

other systems at 23 GeV. The errors are statistical and systematic, respectively.

Hadron Pb+Pb S+Pb S+S p+Pb p+S p+Be p+p

π+ 156±6±23a 165±9±10b 148±4±22a 145±3±10b 139±3±10b 148±3±10b 139±13±21c

K+ 234±6±12a 181±8±10b 180±8±9a 172±9±10b 163±14±10b 154±8±10b 139±15±7c

p 289±7±14d 256±4±10e 208±8±10a 203±6±10e 175±30±10e 156±4±10e 148±20±7c

Λ 289±8±29f — — 203±9±20g — — —

Λ 287±13±29f — — 180±15±18g — — —

aReference [27] (NA44 Collaboration).bReference [28] (NA44 Collaboration).cReference [33, 34] (ISR).dReference [30] (NA44 Collaboration).eReference [29] (NA44 Collaboration).fReference [31] (WA97 Collaboration).gReference [32] (WA97 Collaboration).

qualitative agreement with expectations from gluon saturation [37]. Single particle spectra

alone, however, are not sufficient to disentangle saturation from flow effects.

It is often stated that mT scaling holds in pp collisions at similar√

s to RHIC [see data, for

example, in references [35] and [36]]. Scaling in mT , i.e. spectra following a universal curve

in mT , might be expected if the hadrons are emitted from a source in thermal equilibrium.

It is instructive to note that reference [35] states “Although the curves for different particles

do come together, there is no real evidence for any universal behavior in this variable.” Thus,

scaling at the ISR was never claimed by the original authors. In central Au+Au collisions,

the slopes and yields of π, K and p approach each other as well, but figures 15 and 16 also

do not support a truly universal behavior in mT . Therefore the apparent puzzle of how the

data could exhibit both mT scaling and the mass-dependent pT boost characteristic of radial

flow is no puzzle at all, as any “mT scaling” is only very approximate.

(GeV)Tm0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

10% Central+π0π+K

(GeV)Tm0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

10% Central-π0π-K

FIG. 15: The transverse mass distributions of inclusive identified hadrons produced in 10% central

events, including the π0 as measured in the Electromagnetic Calorimeter in PHENIX and published

in [38].

D. SUMMED CHARGED PARTICLE MULTIPLICITY

As a consistency check we compare the measured rapidity densities as given in Section

IVB to previously published pseudorapidity densities of charged particles. The measured

dN/dy for each hadron species is converted to dN/dη, and the total dN/dη is calculated

by summation. Figure 18 shows dN/dη per participant nucleon pair, compared to the

measurement made by PHENIX using the pad chambers alone [26] as well as to PHOBOS

and STAR yields in central collisions [39, 40]. We note that the lines correspond to the fit

of a linear parameterization of Npart and Ncoll to the PHENIX measurement (open circles)

with a = 0.88 ± 0.28 and b = 0.34 ± 0.12 as described in [41]. For the 5% central collisions,

we measure 598± 30, and is comparable to the STAR result of 567± 38 [40], the PHOBOS

result of 555±37 [42], and the PHENIX pad chamber result of 622±41 [26]. The agreement

is excellent, allowing the results of this analysis to be used to decompose the particle type

dependence of the charge particle multiplicity increase with centrality.

(GeV)Tm0 0.5 1 1.5 2 2.5 3 3.5 4

(2 10-4

5% Central-π-K

FIG. 16: The transverse mass distributions of the inclusive identified hadrons produced in the 5%

central events.

V. COMPARISON WITH MODELS

A. HYDRODYNAMIC-INSPIRED FIT

The charged particle pseudorapdity distributions are incompatible with a static thermal

source, but the flat distribution observed in [42] reflects the strong longitudinal motion in the

initial state. Consequently, the longitudinal momentum distribution is not an unambiguous

sign of collective motion. Transverse momentum is, however, generated in the collision, so

collective expansion may be more easily inferred from transverse momentum distributions.

Following the arguments of the previous section, we analyze the particle mT spectra. A

parameterization of the mT distribution of particles emitted from a hydrodynamic expanding

hadron source is used. In order to determine the freeze-out temperature and collective flow

without confusion from hard scattering processes, a limited pT range is used in the fits. We

include only particles with (mT − m0) < 1 GeV in the fit. Pions with (mT − m0) < 0.38

GeV are excluded to avoid resonance decays. All particles are assumed to decouple from

the expanding hadron source [43] at the same freeze-out temperature, Tfo. This procedure

allows us to extract Tfo and the magnitude of the collective boost in the transverse direction.

The inverse slope includes the local temperature of a section of the hadronic matter along

5-15% Centrality-π-K

(GeV)Tm0 0.5 1 1.5 2 2.5 3 3.5 4

102 30-60% Centrality

(GeV)Tm0 0.5 1 1.5 2 2.5 3 3.5 4

FIG. 17: The transverse mass distributions of the inclusive identified hadrons produced in events

with different centralities.

with its collective velocity. The simple exponential fit of Equation 10 treats each particle

spectrum as a static thermal source, and a collective expansion velocity cannot be extracted

reliably from a single particle spectrum. However, the relative sensitivity to the temperature

and collective radial flow velocity differs for different particles. By using the information

from all the particles, the expansion velocity can be inferred. We fit all particle species

simultaneously with a functional form for a boosted thermal source based on relativistic

hydrodynamics[43].

Use of this form assumes that

• all particles decouple kinematically on a freeze-out hypersurface at the same freeze-out

temperature Tfo,

• the particles collectively expand with a velocity profile increasing linearly with the

radial position in the source (i.e., Hubble expansion where fluid elements do not pass

through one another), and

• the particle density distribution is independent of the radial position.

Longitudinally boost invariant expansion of the particle source is also assumed.

partN0 50 100 150 200 250 300 350 400

Kpπ η/dchdNPHENIXSTARPHOBOS

coll + bNpart = aNη/dchdN

FIG. 18: Both the total charged multiplicity (open) in References [39, 40, 41] and the total iden-

tified charged multiplicity (closed) scaled by the number of participant pairs are plotted together

as a function of the number of participants. The lines correspond to the fit of a linear parameter-

ization of Npart and Ncoll to the PHENIX charged multiplicity measurement (open circles) with

a = 0.88 ± 0.28 and b = 0.34 ± 0.12 as described in [41].

The transverse velocity profile is parameterized as:

βT (ξ) = βmaxT ξn, (13)

where ξ = rR, and R is the maximum radius of the expanding source at freeze-out (0 < ξ < 1)

[44]. The maximum surface velocity is given by βmaxT , and for a linear velocity profile, n =

1. The average of the transverse velocity is equal to:

〈βT 〉 =

βmaxT ξnξdξ∫

ξdξ=

2 + nβmax

T . (14)

Each fluid element is locally thermalized and receives a transverse boost ρ that depends on

the radial position as:

ρ = tanh−1 (βT (ξ)) . (15)

The mT dependence of the invariant yield dNmT dmT

is determined by integrating over the

rapidity, azimuthal angle, and radial distribution of fluid elements in the source. This

procedure, discussed in Appendix C, yields

mT dmT dy= (16)

A∫ 10 mT f(ξ)K1

mT cosh(ρ)Tfo

pT sinh(ρ)Tfo

ξdξ.

The parameters determined by fitting Equation 16 to the data are the freeze-out temperature

Tfo, the normalization A, and the maximum surface velocity βmaxT using a flat particle density

distribution (i.e., f(ξ) = 1).

To study the parameter correlations, we make a grid of combinations of temperature and

velocity, and perform a chi-squared minimization to extract the normalization, A, for each

particle type. The fit is done simultaneously for all particles in the range (mT − m0) < 1

GeV. In addition to this upper limit in the fit, the pion fit range includes a lower limit of

(mT −m0) > 0.38 GeV to avoid the resonance contribution to the low pT region (see Section

The radial flow velocity and freeze-out temperature for all centralities are determined in

the same way. The results are plotted together with the spectra in Figure 19. The hydro-

dynamic form clearly describes the spectra better than the simple exponential in Figure 14.

The values for Tfo and βmaxT are tabulated in Table VI.

TABLE VI: The minimum χ2 and the parameters Tfo and βmaxT for each of the five centrality

selections. The best fit parameters are determined by averaging all parameter pairs within the 1σ

contour. The errors correspond to the standard deviation of the parameter pairs within the 1σ χ2

contour. It is important to note that the fit range in Figure 19 is the same as was used to fit mT

exponentials to the spectra in Figure 14.

Centrality (%) χ2/dof Tfo (MeV) βmaxT < βT >

0-5 34.0/40 121 ± 4 0.70 ± 0.01 0.47±0.01

5-15 34.7/40 125 ± 2 0.69 ± 0.01 0.46±0.01

15-30 36.2/40 134 ± 2 0.65 ± 0.01 0.43±0.01

30-60 68.9/40 140 ± 4 0.58 ± 0.01 0.39±0.01

60-92 36.3/40 161±1912 0.24±0.16

0.2 0.16±0.160.2

Figure 20 shows χ2 contours for the temperature and velocity parameters for the 5% most

central collisions. The n-sigma contours are labeled up to 8σ. The χ2 contours indicate

0 0.5 1 1.5 2 2.510

0 0.5 1 1.5 2 2.5

0-5% (x 5)5-15 (x 2)15-3030-6060-92

0 0.5 1 1.5 2

1/(2 10

0 0.5 1 1.5 2

(GeV/c)Tp0 0.5 1 1.5 2 2.5 3 3.5

FIG. 19: The parameterization and the pT hadron spectra for all five centrality selections.

strong anti-correlation of the two parameters. If the freeze-out temperature decreases, the

flow velocity increases. The minimum χ2 is 34 and the total number of degrees of freedom

(dof) is 40. The parameters that correspond to this minimum are Tfo = 121 ± 4MeV and

βmaxT = 0.70 ± 0.01. The quoted errors are the 1σ contour widths of ∆βmax

T and ∆Tfo.

Within 3σ, the Tfo range is 106 − 141 MeV and the βmaxT range is 0.75 − 0.64.

As a linear velocity profile (n = 1 in Equation 13) is assumed, the mean flow velocity

in the transverse plane is 〈βT 〉 = 2βmaxT /3. If a different particle density distribution (for

instance, a Gaussian function for f(ξ)) were used, then the average should be determined

after weighting accordingly [44].

A similar analysis for Pb+Pb collisions at 158 A GeV, was reported by the NA49 Collab-

oration in [45]. Using the same hydrodynamic parameterization, simultaneous fits of several

hadron species for the highest energy results in Tfo = 127 ± 1 MeV and βmaxT = 0.48 ± 0.01

with χ2/NDF = 120/43 for positive particles and Tfo = 114±2 MeV and βmaxT = 0.50±0.01

maxTβ

0.4 0.5 0.6 0.7 0.8

σ1σ2σ3

σ4σ5

σ6σ7

maxTβ

0.1 0.2 0.3 0.4 0.5

FIG. 20: The χ2 contours in the parameter space Tfo and βmaxT that result after simultaneously

fitting hadrons in the 0 − 5% centrality (top) and 60 − 92% (bottom). The n-sigma contours are

with χ2/NDF = 91/41 for negative particles (statistical errors only). Pions and deuterons

are excluded from the fits to avoid dealing with resonance contributions to the pion yield

and formation of deuterons by coalescence. The φ meson is included in the fit together with

the negative particles. Previously, NA49 used a different parameterization to fit the charged

hadron and deuteron spectra, as well as the mT dependence of measured HBT source radii,

resulting in overlapping χ2 contours with Tfo = 120± 12 MeV and βmaxT = 0.55± 0.12 [46].

1. VELOCITY AND PARTICLE DENSITY PROFILE

In order to use βmaxT and Tfo from the fits described above, one needs to know their

sensitivity to the assumed velocity and particle density profiles in the emitting source. The

choice of a linear velocity profile within the source is motivated by the profile observed in a

full hydrodynamic calculation [47], which shows a nearly perfect linear increase of β(r) with

r. Nevertheless, we also used a parabolic profile to check the sensitivity of the results to

details of the velocity profile. For a parabolic velocity profile (n = 2 in Equation 13), βmaxT

increases by ≈ 13% and Tfo increases by ≈ 5%.

A Gaussian density profile used with a linear velocity profile increases βmaxT by ≈ 2%,

with a neglible difference in the temperature Tfo. As a test of the assumption that all the

particles freeze out at a common temperature, the simultaneous fits were repeated without

the kaons. The difference in Tfo is within the measured uncertainties.

2. INFLUENCE OF RESONANCE PRODUCTION

The functional forms given by Equations 10 and 17 do not include particles arising from

resonance or weak decays. As resonance decays are known to result in pions at low transverse

momenta [48, 49, 50], we place a pT threshold of 500 MeV/c on pions included in the

hydrodynamic fit. A similar approach was followed by NA44, E814, and other experiments

at lower energies, which performed in-depth studies of resonance decays feeding hadron

spectra. However, these were for systems with higher baryon density, so we performed a

cross check on possible systematic uncertainties arising from the pion threshold used in the

fits. To estimate the effect of resonance decays were they not excluded from the fit, we

calculate resonance contributions following Wiedemann [51].

In order to reproduce the relative yields of different particle types, a chemical freeze-out

temperature – different from the kinetic freeze-out temperature – and a baryonic chemical

potential are introduced. Direct production and resonance contribution are calculated for

pions and (anti)protons assuming a kinetic freeze-out temperature of 123 MeV, a transverse

flow velocity of 0.612 (equivalent to 〈βT 〉 = 0.44), a baryon chemical potential of 37 MeV,

and a chemical freeze-out temperature (when particle production stops) of 172 MeV. These

parameters are chosen as they provide a reasonable description of the (anti)proton and pion

spectra and yields (10% most central) and are in good agreement with chemical freeze-

out analyses [52]. Most spectra from resonance decays show a steeper fall-off than the

direct production, which should lead to a smaller apparent inverse slope, depending on what

fraction of the low pT part of the spectrum is included in the fits.

To measure the effect of resonance production on the spectral shape, the local slope is

determined. For a given mT bin number i, the local slope is defined as

Tlocal (i) = − mT (i + 1) − mT (i − 1)

log[N(i + 1)] − log[N(i − 1)], (17)

which is identical to the inverse slope independent of mT for an exponential.

The difference in the local slope,

∆Tlocal = T directlocal − T incl

local, (18)

is determined for direct and inclusive pions and (anti)protons. The differences are plotted

as a function of mT −m0 in Figure 21. The difference in local slope for protons is below 13

MeV for the full transverse mass range; the non-monotonic behavior for protons is caused

by the relatively strong transverse flow. For pions, ∆Tlocal decreases monotonically with mT

and is below 10 MeV above mT = 1GeV/c. A fit of an exponential to the pion spectra for

(mT −m0) > 0.38 GeV (which corresponds to pT > 0.5 GeV/c) yields a difference in inverse

slope of 16 MeV with and without resonances.

B. COMPARISON WITH HYDRODYNAMIC MODELS

Hydrodynamic parameterizations as used in the previous Section rely upon many simpli-

fying assumptions. Another approach to the study of collective flow is to compare the data

to hydrodynamic models. Such models assume rapid equilibration in the collision and de-

scribe the subsequent motion of the matter using the laws of hydrodynamics. Large pressure

∆Tlo

eV) 30

mT-m0 (GeV/c)0 0.5 1 1.5 2 2.5 3

FIG. 21: The difference in the local slope for direct and inclusive pions (solid) and (anti)protons

(dashed).

buildup is found, and we investigate this ansatz by checking the consistency of the data with

calculations using a reasonable set of initial conditions. We compare to two separate models,

the hydrodynamics model of Kolb and Heinz [53, 54, 55] and the “Hydro to Hadrons” (H2H)

model of Teaney and Shuryak [56, 57]. The H2H model consists of a hydrodynamics calcu-

lation, followed by a hadronic cascade after chemical freeze-out. The cascade step utilizes

the Relativistic Quantum Molecular Dynamics (RQMD) model, developed for lower energy

heavy ion collisions [58].

In both models, initial conditions are tuned to reproduce the shape of the transverse

momentum spectra measured in the most central collisions, along with the charged particle

yield. Each model also includes the formation and decay of resonances.

In the Kolb and Heinz model, the initial parameters are the entropy density, baryon num-

ber density, the equilibrium time, and the freeze-out temperature which controls the duration

of the expansion. The chemical freeze-out temperature is the temperature at which particle

production ceases. The initial entropy or energy density and maximum temperature are

fixed to match the measured multiplicity for the most central collisions using a parameteri-

zation that is tuned to produce the measured dNch/dη dependence on both Npart and Ncoll.

A kinetic freeze-out temperature of Tfo = 128 MeV is used. Spectra from the Kolb-Heinz

hydrodynamic model are shown in Figure 22 for pions (upper) and for protons (lower) as

dotted lines. The solid lines are the results from the fits described in the previous sec-

tions. The figure thus allows two comparisons. The similarity of the dashed and solid lines

shows that the hydrodynamic-inspired parameterization used to fit the data results in a pT

distribution similar to this hydrodynamic calculation. Comparing the dashed lines to the

data points shows that the hydrodynamic model agrees quite well for most of the centrality

ranges. It is important to note that the model parameters are uncertain at the level of

10%, and, more importantly, the application of hydrodynamics to peripheral collisions may

be less reasonable than for central collisions, as hydrodynamic calculations assume strong

rescattering and a sufficiently large system size (discussed in [55]).

In reference [56, 59], the PHENIX p spectrum shape is well described by the H2H model

with the LH8 equation of state. The cascade step in the H2H model removes the requirement

that all particles freeze out at a common temperature. Thus the freeze-out temperature and

its profile are predicted, rather than input parameters. Furthermore, following the hadronic

interactions explicitly with RQMD removes the need to rescale the particle ratios at the

end of the calculation, as they are fixed by the hadronic cross sections rather than at some

particular freeze-out temperature. The LH8 equation of state includes a phase transition

with a latent heat of 0.8 GeV. In [56, 59], the Ω and the φ are shown to decouple from the

expanding system at T = 160 MeV, and they receive a flow velocity boost of 0.45c. Pions

and kaons decouple at T = 135 MeV with flow velocity = 0.55c, while protons have T = 120

MeV and flow velocity ≥ 0.6. These temperatures and flow velocities are consistent with

0 0.5 1 1.5 2 2.5

HydroParam. Fit

0 0.5 1 1.5 2 2.5

0-5% (x 5)5-15 (x 2)15-3030-6060-92

(GeV/c)Tp0 0.5 1 1.5 2 2.5 3 3.5

FIG. 22: The hydrodynamics calculation with initial parameters tuned to match the most central

spectra in the pT range 0.3 − 2.0 GeV/c.

the values extracted from the data for the most central events. However, the average initial

energy density exceeds the experimental estimate using formation time τ0 =1 fm/c.

In Figure 23, radial flow from the fits of the previous section are shown as a function

of the number of participants for Tfo (top) and 〈βT 〉 (bottom). There is a slight decrease

of Tfo, while 〈βT 〉 increases with Npart, saturating at 0.45. The value of 〈βT 〉 from Kolb

and Heinz is also shown, and agrees with the data reasonably well. In the plot of 〈βT 〉, the

dashed line indicates the results of fitting the parameterization to the data while keeping

Tfo fixed at 128 MeV to agree with the value used by Kolb and Heinz. Radial flow values for

central collisions remain unchanged, while those in peripheral collisions increase. Even with

the extreme assumption that all collisions freeze out at the same temperature, regardless of

centrality, the trend in centrality dependence of the radial flow does not change.

200Param. FitHydro

partN0 50 100 150 200 250 300 350 400

T = 128 MeVParam. Fit

FIG. 23: The expansion parameters Tfo and βmaxT as a function of the number of participants.

As a comparison, the results from a hydrodynamic model calculation are also shown (Ref. [53, 54,

55]). The dashed line corresponds to a fixed temperature of 128 MeV for all centralities in the

parameterized fit to the data.

C. HYDRODYNAMIC CONTRIBUTIONS AT HIGHER pT

We use the parameters extracted from the fit to the charged hadron spectra in the low pT

region to extrapolate the effect of the soft physics to higher pT . This yields a prediction for

the spectra of hadrons should a collective expanding thermal source be the only mechanism

for particle production in heavy ion collisions. Comparing this prediction to the measured

spectrum of charged particles or neutral pions should indicate the pT range over which soft

thermal processes dominate the cross section. Where the data deviate from the hydrody-

namic extrapolation, other contributions, as e.g. from hard processes or non-equilibrium

production become visible. The approach described here differs from hydrodynamic fits to

(GeV/c)Tp

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-+h+h±+p±+K±πradial flow fit

-π++πradial flow fit -+K+radial flow fit K

pradial flow fit p+

= 0.70maxTβ

= 121 MeVfoT

FIG. 24: The high pT hadron spectra in Reference [38] compared to the fit results assuming radial

flow from the πKp spectra in the 5% central events.

the entire hadron spectrum, as we fix the parameters from the low pT region alone, where

soft physics should be dominant.

The hadron spectrum is calculated using the fit parameters from the low pT region fits

shown in the preceding section, and extrapolated to higher pT . Figure 24 shows the calcu-

lated spectrum for each particle type, and the sum of the extrapolated spectra is compared

to the measured charged hadrons (h+ + h−) in the 5% most central collisions. As non-

identified charged hadrons are measured in η rather than in y, the extrapolated spectra are

converted to units of η. This conversion is most important in the low pT region. No addi-

tional scale factor is applied – the extrapolation and data are compared absolutely. Below

≈ 2.5 GeV/c pT , the agreement is very good, while at higher pT the data begin to exceed

the hydrodynamic extrapolation.

Other hydrodynamic calculations have been successful in describing the distributions

over the full pT range [60] with different parameter values. There are clear indications that

particle production from a hydrodynamic source, if invoked to explain the spectra at low pT ,

will have a non-negligible influence even at relatively large pT . Furthermore, the range of pT

populated by hydrodynamically boosted hadrons is species dependent. This is clearly visible

in Figure 24, which shows that the extrapolated proton spectra have a flatter pT distribution

than the extrapolated pions and kaons. The yield of the “soft” protons reaches, and even

exceeds, that of the extrapolated “soft” pions at 2 GeV/c pT . Therefore the transition from

soft to hard processes must also be species dependent, and the boost of the protons causes

the region where hard processes dominate the inclusive charged particle spectrum to be

at significantly higher transverse momenta in central Au+Au than in p+p collisions. Our

analysis suggests this occurs not lower than pT = 3 GeV/c.

D. HADRON YIELDS AS A FUNCTION OF CENTRALITY

The previous discussion focused on the hadron spectra; now we turn to the centrality

dependence of the pion, kaon, proton, and antiproton yields, which can shed further light

on the importance of different mechanisms in particle production. It is instructive to see

whether yields of the different hadrons scale with the number of participant nucleons, Npart,

the number of binary nucleon-nucleon collisions, Ncoll, or some combination of the two.

The total yields of the hadrons may be expected to be dominated by soft processes, and

the wounded nucleon model of soft interactions suggests that the yields should scale as the

number of participants, Npart. If each participant loses a certain fraction of its incoming

energy, like e.g. in string models, where each pair of participants (or wounded nucleons)

contributes a color flux tube, the total energy of the fireball formed at central rapidity would

be proportional to the number of participants Npart. If, furthermore, the fireball is locally

thermalized and particle production is determined at a single temperature, the multiplicity

would scale with Npart. On the other hand, at very high pT , particle production may be

dominated by hard processes and scale with Ncoll[61, 62].

In order to investigate the existence of scaling, the multiplicities are parameterized as:

dy= C · (Npart)

αpart (19)

TABLE VII: Fit parameters for each particle species using equations 19 and 20.

particle αpart αcoll

π+ 1.06 ± 0.01 0.79 ± 0.01

π− 1.08 ± 0.01 0.80 ± 0.01

K+ 1.18 ± 0.02 0.88 ± 0.02

K− 1.20 ± 0.03 0.89 ± 0.02

p+ 1.16 ± 0.02 0.86 ± 0.02

p− 1.14 ± 0.03 0.84 ± 0.02

dy= C ′ · (Ncoll)

αcoll. (20)

Fit results for these parameterizations are shown in Table VII. As can be seen, the exponents

αpart are > 1 for all species, while αcoll is consistently < 1. The production of all particles

increases more strongly than with Npart, but not as strongly as with Ncoll. Small differences

between the different particle species are apparent: The (anti-)proton yield increases more

strongly than the pion yield, and the kaon yield shows the strongest centrality dependence.

Remarkably, the yield fraction scaling beyond linear with Npart is larger for kaons, protons,

and antiprotons than for pions. Perhaps it is not surprising that the yields do not scale

simply with Npart; the collective flow seen in the pT spectra already shows that the nucleon-

nucleon collisions cannot be independent.

We next check whether the simple model of hadron yields can be brought into agreement

with the data by adding a component of the yields scaling as the number of binary collisions,

Ncoll. Such an admixture inspires simple two-component models [61, 62]. The nonlinearity

of dN/dy on the number of participants is illustrated by the ratio (dN/dy)/Npart, shown in

Figure 25 as a function of centrality. The yields are seen to depend linearly on Ncoll/Npart.

As seen already from the exponents in Table VII, the increase with centrality is strongest for

kaons, intermediate for (anti-)protons, and weakest for pions. This indicates that protons

and antiprotons have a larger component scaling with Ncoll than pions.

We fit the yields per participant with Equation 21. As in [61, 62] we parameterize the

multiplicity using two free parameters: npp, the multiplicity in p+p collisions, and x, the

relative strength of the component scaling with Ncoll.

R ≡ dN/dy

Npart= (1 − x) · npp

2+ x · npp

Npart− 1

. (21)

The results of the fit are shown as solid lines in Figure 25. The fit parameter values are given

in Table VIII. All hadron species are well fit. The importance of the component scaling as

Ncoll is largest for kaons and smallest for pions.

TABLE VIII: Values of the parameters npp and x from fitting Equation 21 to the observed dN/dy

per Npart.

π+ 1.41 ± 0.11 0.028 ± 0.020

π− 1.10 ± 0.11 0.085 ± 0.030

K+ 0.130 ± 0.021 0.232 ± 0.076

K− 0.089 ± 0.020 0.326 ± 0.132

p 0.089 ± 0.013 0.181 ± 0.062

p 0.062 ± 0.010 0.172 ± 0.068

We check the consistency of the fits in Figure 25 with known hadron yields in p+p

collisions by extrapolating the fits down to two participants (and one binary nucleon-nucleon

collision). Isospin differences between p+p and Au+Au are ignored. The check is done by

separately extrapolating the fitted fraction of yield which scales with Ncoll and the fraction

scaling with Npart down to one nucleon-nucleon collision and two participant nucleons, and

summing the result. One obtains particle ratios of K/π = (8.7 ± 2.6)% and p/π = (4.9 ±0.8)%. These values fall between those measured at lower

√s at the ISR [63] and those at

higher√

s at the Tevatron [64], as expected since the RHIC energy lies in between. Thus

the Au+Au data are shown to scale down to p+p reasonably.

One may expect that the particle ratios at very high pT should be dominated by hard

scattering, and therefore scale with the number of binary collisions. Consequently, we look

at ratios of the Ncoll scaling components alone, extrapolated down to one binary collision.

The values are compared to measurements of hadron ratios at the ISR [65] in Figures 26

0.5 1 1.5 2 2.5 3

Ncoll/Npart

K-(x20)K-(x20)

π-π-

p (x20)

K+(x20)K+(x20)

π+π+

p (x20)

FIG. 25: dN/dy per participant of different particle species as a function of the number of collisions

per participant. Kaon and (anti-)proton multiplicities are scaled by a factor of 20.

and 27. The ratio of the extrapolated Au+Au yield fractions scaling as Ncoll are shown as

solid lines for pT ≥ 2 GeV/c. The agreement with the p+p data at high pT is quite good.

Finally, we directly compare p/π and p/π ratios in central Au+Au collisions with p+p,

as a function of pT . These ratios from the 10% most central data, using the charged particle

measurement from this paper and neutral pions from [38], are shown in Figure 28. The

ratios show a steady increase up to 2.5 GeV/c in pT . Even though the simple extrapolation

(GeV/c)T

p0 1 2 3 4 5

1.2 Alper et.al. NP B100,237,(1975)

23 GeV31 GeV45 GeV53 GeV63 GeV

FIG. 26: Kaon to pion ratio as a function of pT . The different points are measured in p+p collisions

(data from ref. [65]). The solid line is the asymptotic value for high pT in p+p derived from the

hard scattering component of the fits using Equation 21 to the measured centrality dependence

of dN/dy in Au-Au collisions at√

sNN = 130 GeV. The dashed lines indicate the corresponding

uncertainty.

of the Ncoll scaling yield fraction agreed with p+p, the ratios of the full yield significantly

exceed those in the ISR measurements [65]. According to Gyulassy and collaborators, [66],

this result may give insight into baryon number transport and the interplay between soft

and hard processes.

Of course, splitting the observed yields into portions which scale with Npart and Ncoll

is by no means a unique explanation of the data. The spectra and yields can also be

well reproduced by thermal models, which break such simple scalings due to the multiple

interactions suffered by the constituents.

Simple thermal models that ignore transverse and longitudinal flow [67] are able to de-

scribe the centrality dependence of the mid-rapidity π±, K±, p, and p yields by tuning the

chemical freeze-out temperature Tch, the baryon chemical potential µB and by introducing

a strangeness saturation factor γs. It was found that µB is independent of centrality, while

both γs and Tch increase from peripheral to central collisions. Within the same model, the

centrality dependence of the particle yields at lower energy (√

sNN = 17 GeV [68, 69]) are

described by constant Tch and µB. The strong centrality dependence in kaon production

at both energies is accounted for by the increase in the strangeness saturation factor γs.

Although the integrated particle yields are very well described, such simple thermal models

(GeV/c)T

p0 1 2 3 4 5

1.2 Alper et.al. NP B100,237,(1975)

23 GeV31 GeV45 GeV53 GeV63 GeV

FIG. 27: Antiproton to π− ratio as a function of pT . The different points are measured in p + p

collisions (data from ref. [65]). The solid line is the asymptotic value for high pT in p+p derived

from the hard scattering component of the fits using Equation 21 to the measured centrality

dependence of dN/dy in Au-Au collisions at√

sNN = 130 GeV. The dashed lines indicate the

corresponding uncertainty.

(GeV/c)T

p0 1 2 3 4 5 0 1 2 3 4 5

5 +πp / 0πp /

, pp @53 GeV, ISR +πp /

(GeV/c)T

5 -π / p0π / p

, pp @53 GeV, ISR -π / p

FIG. 28: a) Proton to pion ratio as a function of pT . b) Antiproton to pion ratio as a function

of pT . The open circles represent measurements in p + p collisions (data from ref. [65]). The filled

circles show the 10 % most central Au+Au collisions. The neutral pion spectra are from the data

published in [38].

do not attempt a comparison to the single particle spectra, which clearly indicate centrality

dependent flow effects not included in the model.

Thermal models which include hydrodynamical parameters on a freeze-out hypersurface

to account for longitudinal and transverse flow can reproduce the absolutely normalized

particle spectra by introducing only two thermal parameters Tch and µB [70, 71]. In

this approach, the thermal parameters are independent of centrality, while the geometric

parameters are adjusted to reproduce the spectra. Good agreement with the data is obtained

up to pT ≈ 2 − 3 GeV/c, however an explicit comparison with the centrality dependence of

the integrated mid-rapidity yields has not yet been made.

This section shows that the yields of all hadrons increase more rapidly than linearly with

the number of participants, but the increase is weaker than scaling with the number of binary

collisions. The excess beyond linear scaling with Npart is strongest for kaons, intermediate

for (anti-)protons, and weakest for pions. The centrality dependence of the total yields can

be well fit with a sum of these two kinds of scaling. At high pT , the baryon and anti-baryon

yields greatly exceed expectations from p+p collisions. Thermal models, which do not invoke

strict scaling rules, can successfully reproduce the data as well, providing that they include

the radial flow required by the pT spectra.

VI. SUMMARY AND CONCLUSION

We have presented the spectra and yields of identified hadrons produced in√

130 GeV Au + Au collisions. The yields of pions increase approximately linearly with

the number of participant nucleons, while the yield increase is faster than linear for kaons,

protons, and antiprotons.

Hydrodynamic analyses of the particle spectra are performed: the spectra are fit with a

hydrodynamic-inspired parameterization to extract freeze-out temperature and radial flow

velocity of the particle source. The data are also compared to two full hydrodynamics

calculations. The simultaneous fits of pion, kaon, proton, and antiproton spectra show that

radial flow in central collisions at RHIC exceeds that at lower energies and increases with

centrality of the collision. The hydrodynamic models are consistent with the measured

spectral shapes, extracted freeze-out temperature Tfo, and the flow velocity βT in central

collisions.

Extrapolating the fits to estimate thermal particle production at higher pT allows us

to study the soft-hard physics boundary by comparing to measured spectra at high pT .

The yield of the “soft” protons reaches, and even exceeds, that of the extrapolated “soft”

pions at 2 GeV/c pT . The sum of the extrapolated “soft” spectra agree with the measured

inclusive data to pT ≈ 2.5 − 3 GeV/c. The transition from soft to hard processes must be

species dependent, and the admixture of boosted nucleons implies that hard processes do

not dominate the inclusive charged particle spectra until approximately 3 GeV/c.

APPENDIX A: DETERMINING Npart AND Ncoll

As only the fraction of the total cross section is measured in both the ZDC and BBC

detectors, a model-dependent calculation is used to map collision centrality to the number of

participant nucleons, Npart, and the number of nucleons undergoing binary collisions, Ncoll.

A discussion of this calculation at RHIC can be found elsewhere [61].

Using a Glauber model combined with a simulation of the BBC and ZDC responses, Npart

and Ncoll are determined in each centrality. The model provides the thickness of nuclear

matter in the direct path of each oncoming nucleon, and uses the inelastic nucleon-nucleon

cross section σinelN+N to determine whether or not a nucleon-nucleon collision occurs. We

assume the following:

• The nucleons travel in straight-line paths, parallel to the velocity of its respective

nucleus.

• An inelastic collision occurs if the relative distance between two nucleons is less than√

σinelN+N/π.

• Fluctuations are introduced by using the simulated detector response for both the

ZDC and BBC.

In this calculation, the Woods-Saxon nuclear density distribution (ρ(r)) is used for each

nucleus with three parameters, the nuclear radius R = 6.38+0.27−0.13 fm, diffusivity d = 0.53±0.01

fm [15], and the inelastic nucleon-nucleon cross section σinelN+N = 40 ± 3 mb,

ρ(r) =ρ0

1 + er−rn

. (A1)

APPENDIX B: INVARIANT CROSS SECTIONS

Tabulated here are the measured invariant yields of pions, kaons, and (anti)protons pro-

duced in Au+Au collisions at 130 GeV. The first set of tables (Tables IX- XII) are the

TABLE IX: Invariant yields for π±, K±, and (anti)p measured in minimum bias events at midra-

pidity and normalized to one rapidity unit. The errors are statistical only.

pT (GeV/c) π± K± p(p)

0.25 112±2

109±2

0.35 56 ±1

49.9 ±0.9

0.45 28.0 ±0.5 6.1±0.4

24.1 ±0.5 4.6±0.4

0.55 15.7 ±0.3 4.0±0.3 2.3± 0.1

14.6 ±0.3 3.2±0.2 1.2±0.1

0.65 9.1 ±0.2 2.8±0.2 1.8± 0.1

8.7 ±0.2 2.1 ±0.2 1.17± 0.09

0.75 5.8 ±0.1 1.7±0.1 1.38± 0.08

5.6 ±0.2 1.6±0.1 0.98±0.07

0.85 3.8 ±0.1 1.30±0.08 1.18±0.07

3.6±0.1 1.17±0.09 0.95±0.07

0.95 2.40 ±0.08 0.87±0.06 0.98± 0.06

2.28 ±0.08 0.69±0.06 0.65± 0.05

1.05 1.61 ±0.06 0.62±0.04 0.70± 0.04

1.61 ±0.06 0.53±0.05 0.50± 0.04

1.15 1.03 ±0.04 0.43±0.03 0.60± 0.04

1.17 ±0.05 0.38±0.04 0.35± 0.03

1.25 0.71±0.03 0.33±0.03 0.41± 0.03

0.76 ±0.04 0.27±0.03 0.34±0.03

1.35 0.46 ±0.02 0.20±0.02 0.32±0.02

0.54±0.03 0.16±0.02 0.22±0.02

1.45 0.35±0.02 0.17±0.02 0.23± 0.02

0.31 ±0.02 0.13±0.02 0.18± 0.02

1.55 0.24 ±0.02 0.10±0.01 0.17± 0.02

0.22 ±0.02 0.10±0.01 0.15± 0.02

1.65 0.16 ±0.01 0.08±0.01

0.15 ±0.01 0.07±0.01

invariant cross sections plotted in Figures 9 and 10. The second set of tables (Tables XIII-

XVI) are the invariant cross sections in equal pT bins as used in Figure 11.

APPENDIX C: FREEZE-OUT SURFACE ASSUMPTIONS

The freeze-out surface is σ (r, φ, η), where the radius r is between zero and R, the radius

at freeze-out, the azimuthal angle φ is between zero and 2π, and the longitudinal space-time

rapidity variable η varies between −ηmax and ηmax. In the Bjorken scenario, the freeze-out

surface in space-time is hyperbolic, with contours of constant proper time τ =√

t2 − z2.

Assuming instantaneous freeze-out in the radial direction and longitudinal boost-invariance,

the model-dependence factors out of Equation 17 and is included in the normalization

constant A.

At 130 GeV, the PHOBOS experiment measures the total charged particle pseudorapidity

distribution to be flat over 2 units of pseudorapidity [42]. The measured rapidity in PHOBOS

is taken to be the same as the rapidity of the fireball, defined here as z. The rapidity variables

in the integrand vanish for |z| > 2. Therefore, the integration over the fireball rapidity is

generally taken to be from −∞ to +∞ using the modified K1 Bessel function

K1(mT /T ) =∫ ∞

0cosh(z)e−mT cosh(z)/T dz (C1)

where the variable z is the fireball rapidity variable. The K1 bessel function can also result

by integration over the measured rapidity y with the assumption that the freeze-out is

instantaneous in the radial direction. In this case, no assumption is made on the shape

of the freeze-out hypersurface. This also assumes that the total rapidity distribution is

measured in the detector. What results is the single differential 1/mT dN/dmT .2

ACKNOWLEDGMENTS

We thank the staff of the RHIC Project, Collider-Accelerator, and Physics Departments

at Brookhaven National Laboratory and the staff of the other PHENIX participating institu-

tions for their vital contributions. We acknowledge support from the Department of Energy,

Office of Science, Nuclear Physics Division, the National Science Foundation, and Dean of the

2 Private communication with U. Heinz.

TABLE X: Pion invariant yields in each event centrality and pT bin measured at midrapidity,

normalized to one rapidity unit. For each measured pT bin, the positive pion cross section is the

top row and the negative pion cross section is the bottom row. Errors are statistical only.

pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92%

0.25 355 ± 9 282 ± 6 186 ± 4 81 ± 2 13.2 ± 0.5

371 ± 10 275 ± 7 180 ± 4 74 ± 2 12.1 ± 0.5

0.35 188 ± 5 146 ± 3 93 ± 2 36.6 ± 0.8 5.3 ± 0.2

169 ± 5 128 ± 3 82 ± 2 34.3 ± 0.9 5.0 ± 0.2

0.45 95 ± 3 74 ± 2 48 ± 1 17.5 ± 0.5 2.7 ± 0.1

86 ± 3 63 ± 2 40 ± 1 15.7 ± 0.5 2.1 ± 0.1

0.55 56 ± 2 41 ± 1 26.0 ± 0.7 10.1 ± 0.3 1.32 ± 0.09

51 ± 2 38 ± 1 24.5 ± 0.8 9.6 ± 0.3 1.18 ± 0.09

0.65 32± 1 25.6 ± 0.8 15.0 ± 0.5 5.3 ± 0.2

30 ± 1 22.6 ± 0.8 14.5 ± 0.5 5.7 ± 0.2

0.70 0.62± 0.04

0.57± 0.04

0.75 21.1 ± 0.9 15.4 ± 0.6 9.9 ± 0.4 3.6 ± 0.1

20 ± 1 15.3 ± 0.6 9.5 ± 0.4 3.5 ± 0.2

0.85 14.0 ± 0.7 10.3 ± 0.4 6.4 ± 0.3 2.3 ± 0.1

12.8 ± 0.8 9.6 ± 0.5 6.1 ± 0.3 2.1 ± 0.1

0.90 0.19 ± 0.02

0.24 ± 0.02

1.00 7.1 ± 0.3 5.3± 0.2 3.4 ± 0.1 1.25 ± 0.05

6.5 ± 0.3 5.0 ± 0.2 3.4 ± 0.1 1.25 ± 0.05

1.20 3.2 ± 0.2 2.2 ± 0.1 1.47 ± 0.07 0.55 ± 0.03 0.064 ± 0.006

3.3 ± 0.2 2.6 ± 0.1 1.51 ± 0.08 0.63 ± 0.04 0.061 ± 0.007

1.40 1.3 ± 0.1 1.01 ± 0.07 0.72 ± 0.04 0.27 ± 0.02

1.3 ± 0.1 1.25 ± 0.09 0.72 ± 0.05 0.26 ± 0.02

1.60 0.55 ± 0.07 0.57 ± 0.05 0.33 ± 0.03 0.14 ± 0.01 0.015 ± 0.003

0.51 ± 0.07 0.57 ± 0.05 0.30 ± 0.03 0.12 ± 0.01 0.014 ± 0.003

1.80 0.35 ± 0.05 0.25 ± 0.03 0.15 ± 0.02 0.060 ± 0.008

0.40 ± 0.06 0.27 ± 0.03 0.14 ± 0.02 0.075 ± 0.009

2.00 0.18 ± 0.03 0.13 ± 0.02 0.10 ± 0.01 0.023 ± 0.004 0.005 ± 0.001

TABLE XI: Kaon invariant yields in each event centrality and pT bin, measured at midrapidity

and normalized to one rapidity unit. The top row in each pT bin is K+, and the bottom row is

K−. Errors are statistical only.

pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92%

0.44 0.5 ± 0.1

0.4 ± 0.1

0.45 21± 3 16 ± 2 10 ± 1 4.3 ± 0.5

21± 3 13 ± 2 7 ± 1 2.5 ± 0.4

0.54 0.20 ± 0.07

0.3 ± 0.1

0.55 15± 2 11 ± 1 6.6 ± 0.7 2.4 ± 0.3

13± 2 8 ± 1 4.8 ± 0.6 2.3 ± 0.3

0.65 9 ± 1 7.5 ± 0.7 4.7 ± 0.4 1.9 ± 0.2

8 ± 1 7.0 ± 0.8 3.1 ± 0.4 1.1 ± 0.2

0.69 0.18 ± 0.03

0.14 ± 0.03

0.75 5.3 ± 0.7 4.6 ± 0.5 3.1 ± 0.3 0.9 ± 0.1

5.1 ± 0.8 5.0 ± 0.6 2.5 ± 0.3 0.9 ± 0.1

0.85 5.7 ± 0.7 3.6 ± 0.4 2.1 ± 0.2 0.67 ± 0.08

3.6 ± 0.6 3.7 ± 0.4 2.0 ± 0.2 0.64 ± 0.09

0.89 0.07 ± 0.02

0.09 ± 0.02

0.95 3.0 ± 0.4 2.3 ± 0.2 1.5 ± 0.2 0.51 ± 0.07

2.4 ± 0.4 2.3 ± 0.3 1.0 ± 0.2 0.35 ± 0.06

1.05 2.3 ± 0.3 1.5 ± 0.2 1.2 ± 0.1 0.37 ± 0.05

1.8 ± 0.3 1.8 ± 0.2 0.8 ± 0.1 0.27 ± 0.05

1.15 1.6 ± 0.3 1.3 ± 0.2 0.62 ± 0.09 0.29 ± 0.04

1.4 ± 0.3 0.9 ± 0.2 0.7 ± 0.1 0.23 ± 0.04

1.17 0.012± 0.004

0.015± 0.005

1.25 1.1 ± 0.2 1.0 ± 0.1 0.66 ± 0.09 0.15 ± 0.03

1.2 ± 0.2 0.8 ± 0.1 0.41 ± 0.08 0.15 ± 0.03

1.35 0.6 ± 0.1 0.6 ± 0.1 0.35 ± 0.05 0.12 ± 0.02

TABLE XII: (Anti)proton invariant yields in each event centrality and pT bin, measured at

midrapidity and normalized to one rapidity unit. The top row in each pT is the proton cross

section, and the bottom row the antiproton. The errors are statistical only.

pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92%

0.545 0.26 ± 0.06

0.12 ± 0.05

0.55 8 ± 1 4.9 ± 0.5 4.0 ± 0.4 1.6 ± 0.2

4.2 ± 0.8 2.8 ± 0.5 2.0 ± 0.3 0.8 ± 0.1

0.65 6.3 ± 0.7 4.7 ± 0.4 2.7 ± 0.2 1.2 ± 0.1

4.3 ± 0.7 2.6 ± 0.4 1.9 ± 0.3 0.9 ± 0.1

0.695 0.14 ± 0.02

0.14 ± 0.03

0.75 4.4 ± 0.5 4.0 ± 0.4 2.2 ± 0.2 0.90 ± 0.08

3.6 ± 0.5 2.5 ± 0.3 1.7 ± 0.2 0.60 ± 0.08

0.85 3.9 ± 0.4 3.3 ± 0.3 1.9 ± 0.2 0.75 ± 0.07

2.9 ± 0.5 2.5 ± 0.3 1.8 ± 0.2 0.62± 0.08

0.895 0.10± 0.02

0.06± 0.01

1.00 3.1 ± 0.2 2.4 ± 0.2 1.37 ± 0.09 0.46 ± 0.03

2.1 ± 0.2 1.5 ± 0.1 0.91 ± 0.08 0.41 ± 0.04

1.18 0.031± 0.005

0.018± 0.004

1.20 2.0 ± 0.2 1.4 ± 0.1 0.82 ± 0.06 0.28 ± 0.02

1.4± 0.2 1.0 ± 0.1 0.54 ± 0.05 0.19 ± 0.02

1.40 1.1 ± 0.1 0.74 ± 0.07 0.46 ± 0.04 0.14 ± 0.01

0.9 ± 0.1 0.50 ± 0.06 0.32 ± 0.04 0.13 ± 0.02

1.58 0.005± 0.002

0.007± 0.002

1.60 0.54 ± 0.07 0.49 ± 0.05 0.25 ± 0.03 0.09 ± 0.01

0.49 ± 0.08 0.37 ± 0.05 0.20 ± 0.03 0.053 ± 0.009

1.80 0.34 ± 0.05 0.25 ± 0.03 0.16 ± 0.02 0.047 ± 0.007

0.27 ± 0.06 0.11 ± 0.02 0.10 ± 0.02 0.021 ± 0.005

1.98 0.003 ± 0.001

TABLE XIII: Minimum bias invariant yields for all particles in equal pT bins. For each pT , the

first line are the positive particle yields, and the second are the negative particle yields. The units

are c2/GeV 2.

pT (GeV/c) π± K± (anti)p

0.25 112±2

109±2

0.35 56 ±1

49.9 ±0.9

0.45 28.0 ±0.5 6.1±0.4

24.1 ±0.5 4.6±0.4

0.55 15.7 ±0.3 4.0±0.3 2.3±0.1

14.6 ±0.3 3.2±0.2 0.38±0.02

0.70 7.3 ±0.1 2.18±0.09 1.55±0.06

7.0 ±0.1 1.9±0.1 1.07±0.06

0.90 3.06 ±0.06 1.07±0.05 1.08±0.04

2.89 ±0.07 0.91±0.05 0.79±0.04

1.20 0.91 ±0.02 0.38±0.02 0.49±0.02

0.98 ±0.02 0.32±0.02 0.35±0.01

1.60 0.208 ±0.007 0.104±0.006 0.157±0.007

0.193 ±0.007 0.093±0.006 0.119±0.007

2.00 0.050 ±0.003 0.051±0.003

0.053 ±0.003 0.031±0.003

2.45 0.0028 ±0.0005 0.013±0.001

0.0034 ±0.0006 0.009±0.001

2.95 0.0036±0.0006

0.0022±0.0005

3.55 0.0007±0.0002

0.0006±0.0002

TABLE XIV: Pion invariant yields in each event centrality normalized to one rapidity unit at

midrapidity. The first line corresponds to positive pions, and the second to negative pions.

pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92%

0.25 355±9 282±6 186±4 81±2 13.2±0.5

371±10 275±7 180± 4 74 ± 2 12.1 ± 0.5

0.35 188±5 146±3 93± 2 36.6± 0.8 5.3 ± 0.2

169±5 128±3 82± 2 34.3± 0.9 5.0 ± 0.2

0.45 95±3 74±2 48± 1 17.5± 0.5 2.7 ± 0.1

86±3 63±2 40± 1 15.7± 0.5 2.1 ± 0.1

0.55 56±2 41±1 26.0± 0.7 10.1± 0.3 1.32 ± 0.09

51±2 38±1 24.5± 0.8 9.6 ± 0.3 1.18 ± 0.09

0.70 26.3±0.8 20.2±0.5 12.3± 0.3 4.4 ± 0.1 0.62 ± 0.04

24.7±0.9 18.6±0.6 11.8± 0.4 4.5 ± 0.1 0.57 ± 0.04

0.90 11.0±0.4 7.9 ±0.2 5.1 ± 0.2 1.79 ± 0.06 0.19 ± 0.02

10.0±0.5 7.9 ±0.3 5.0 ± 0.2 1.76 ± 0.07 0.24 ± 0.02

1.20 3.1±0.1 2.37 ±0.09 1.50 ± 0.05 0.58 ± 0.02 0.064 ± 0.006

3.4±0.2 2.7 ±0.1 1.67 ± 0.07 0.64 ± 0.03 0.061 ± 0.007

1.60 0.62±0.05 0.54 ±0.03 0.34 ± 0.02 0.142 ± 0.009 0.015 ± 0.003

0.63±0.06 0.58 ±0.04 0.32 ± 0.02 0.129 ± 0.009 0.014 ± 0.003

2.00 0.17±0.02 0.14 ±0.01 0.083 ± 0.009 0.027 ± 0.003 0.005 ± 0.001

0.20±0.03 0.14 ±0.02 0.09 ± 0.01 0.035 ± 0.004 0.004 ± 0.001

2.45 0.005 ±0.003 0.009 ±0.003 0.006 ± 0.002 0.0017 ± 0.0006

0.011±0.005 0.011 ±0.004 0.005 ± 0.002 0.0025 ± 0.0009

College of Arts and Sciences, Vanderbilt University (U.S.A), Ministry of Education, Culture,

Sports, Science, and Technology and the Japan Society for the Promotion of Science (Japan),

Russian Academy of Science, Ministry of Atomic Energy of Russian Federation, Ministry

of Industry, Science, and Technologies of Russian Federation (Russia), Bundesministerium

fuer Bildung und Forschung, Deutscher Akademischer Auslandsdienst, and Alexander von

Humboldt Stiftung (Germany), VR and the Wallenberg Foundation (Sweden), MIST and

TABLE XV: Kaon invariant yields in each event centrality normalized to one rapidity unit at

midrapidity. The first line corresponds to positive kaons, and the second to negative kaons.

pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92%

0.45 21±3 16± 2 10± 1 4.3 ± 0.5 0.5 ± 0.1

21±3 13± 2 7 ± 1 2.5 ± 0.4 0.4 ± 0.1

0.55 15±2 11± 1 6.6 ± 0.7 2.4 ± 0.3 0.20 ± 0.07

13±2 8 ± 1 4.8 ± 0.6 2.3 ± 0.3 0.3 ± 0.1

0.70 8.0±0.7 6.6 ± 0.5 4.3 ± 0.3 1.5 ± 0.1 0.18 ± 0.03

7.0±0.8 6.5 ± 0.6 3.1 ± 0.3 1.1 ± 0.1 0.14 ± 0.03

0.90 4.5±0.4 3.1 ± 0.2 1.9 ± 0.1 0.62 ± 0.06 0.06 ± 0.02

3.3±0.4 3.3 ± 0.3 1.6 ± 0.2 0.5 ± 0.06 0.09 ± 0.02

1.20 1.4±0.1 1.10 ± 0.08 0.68 ± 0.05 0.22 ± 0.02 0.012 ± 0.004

1.3±0.1 0.97 ± 0.08 0.50 ± 0.05 0.17 ± 0.02 0.015 ± 0.005

1.60 0.36±0.05 0.29 ± 0.03 0.17 ± 0.02 0.062 ± 0.007 0.008 ± 0.002

0.29±0.05 0.27 ± 0.03 0.20 ± 0.02 0.058 ± 0.008 0.004 ± 0.002

the Natural Sciences and Engineering Research Council (Canada), Conselho Nacional de

Desenvolvimento Cientıfico e Tecnologico and Fundacao de Amparo a Pesquisa do Estado

de Sao Paulo (Brazil), Natural Science Foundation of China (People’s Republic of China),

Centre National de la Recherche Scientifique, Commissariat a l’Energie Atomique, Insti-

tut National de Physique Nuclaire et de Physique des Particules, and Association pour la

Recherche et le Developpement des Methodes et Processus Industriels (France), Department

of Atomic Energy and Department of Science and Technology (India), Israel Science Foun-

dation (Israel), Korea Research Foundation and Center for High Energy Physics (Korea),

the U.S. Civilian Research and Development Foundation for the Independent States of the

Former Soviet Union, and the US-Israel Binational Science Foundation.

TABLE XVI: (Anti)proton invariant yields in each event centrality normalized to one rapidity

unit at midrapidity. The first line corresponds to protons, and the second to antiprotons.

pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92%

0.55 8±1 4.9 ± 0.5 4.0 ± 0.4 1.6 ± 0.2 0.26 ± 0.06

4.2±0.8 2.8± 0.5 2.0± 0.3 0.8± 0.1 0.12± 0.05

0.70 5.4±0.4 4.5± 0.3 2.5± 0.2 1.06± 0.07 0.14± 0.02

4.4±0.5 2.9± 0.3 2.0± 0.2 0.80± 0.08 0.14± 0.03

0.90 3.9±0.3 3.1± 0.2 1.9± 0.1 0.71± 0.05 0.10± 0.02

2.8±0.3 2.1± 0.2 1.4± 0.1 0.58± 0.05 0.06± 0.01

1.20 1.9±0.1 1.37± 0.08 0.78± 0.04 0.26± 0.02 0.031± 0.005

1.3±0.1 0.96± 0.07 0.56± 0.04 0.21± 0.02 0.018± 0.004

1.60 0.60±0.06 0.44± 0.03 0.27± 0.02 0.087± 0.008 0.005± 0.002

0.49±0.06 0.34± 0.03 0.19± 0.02 0.062± 0.007 0.007± 0.002

2.00 0.20±0.03 0.15± 0.02 0.09± 0.01 0.025± 0.003 0.003± 0.001

0.15±0.03 0.07± 0.01 0.055± 0.009 0.019 ± 0.003 0.0005± 0.0005

2.45 0.06±0.01 0.040± 0.007 0.020 ± 0.004 0.006± 0.001 0.0010± 0.0006

0.04±0.01 0.028± 0.006 0.011± 0.003 0.005± 0.001 0.0020 ± 0.0008

2.95 0.015±0.005 0.007± 0.002 0.005± 0.002 0.0023± 0.0007 0.0006± 0.0004

0.013±0.005 0.008± 0.003 0.002± 0.001 0.0003± 0.0003 0.0005± 0.0003

3.55 0.003 ±0.002 0.0012 ± 0.0007 0.0014± 0.0006 0.0005± 0.0002

0.002±0.001 0.0011± 0.0007 0.0013± 0.0006 0.0002± 0.0002

[1] B. Andersson et al., Phys. Rep. 97, 31 (1983).

[2] X. Artru, Phys. Rep. 97, 147 (1983).

[3] J. Owens et al., Phys. Rev. D 18, 1501 (1978).

[4] K. Ackermann et al., Phys. Rev. Lett. 86, 402 (2001).

[5] C. Adler et al., Phys. Rev. Lett. 87, 182301 (2001).

[6] C. Adler et al., Phys. Rev. C 66, 034904 (2002).

[7] C. Adler et al., Phys. Rev. Lett. 90, 032301 (2003).

[8] K. Adcox et al., Phys. Rev. Lett. 89, 212301 (2002).

[9] B. Back et al., Phys. Rev. Lett. 89, 222301 (2002).

[10] D. Morrison et al., Nucl. Phys. A 638 (1998).

[11] W. Zajc, Nucl. Phys. A 698, 39 (2002).

[12] K. Adcox et al., Nucl. Instr. Meth. A (2001), accepted for publication.

[13] J. Mitchell et al., Nucl. Instrum. Meth. A 482, 491 (2002).

[14] C. Adler et al., Nucl. Instrum. Meth. A 470, 488 (2001).

[15] R. Glauber and J. Natthiae, Nucl. Phys. B 21, 135 (1970).

[16] B. Hahn, D. Ravenhall, and R. Hofstadter, Phys. Rev. 101, 1131 (1956).

[17] S. J. Pollack et al., Phys. Rev. C 46, 2587 (1992).

[18] D. Groom, Euro. Phys. Journ. C 3, 144 (1998).

[19] R. Brun, R. Hagelberg, N. Hansroul, and J. Lassalle, CERN-DD-78-2 (1978).

[20] J. M. Burward-Hoy, Ph.D. thesis, State University of New York at Stony Brook (2001).

[22] R. Albrecht et al., Eur. Phys. J. C 5, 255 (1998).

[23] M. Aggarwal et al., Eur. Phys. J. C 23, 225 (2002).

[24] M. Faessler, Phys. Repts. 115, 1 (1984).

[27] I. Bearden et al., Phys. Rev. Lett. 78, 2080 (1997).

[28] H. Boggild et al., Phys. Rev. C 59, 328 (1999).

[29] I. Bearden et al., Phys. Rev. C 57, 837 (1998).

[30] I. Bearden et al., Phys. Lett. B 388, 431 (1996).

[31] E. Andersen et al., Journ. Phys. G 25, 171 (1999).

[32] F. Antinori et al., Phys. Lett. B 433, 209 (1998).

[33] B. Alper et al., Nucl. Phys. B 100, 237 (1975).

[34] K. Guettler et al., Nucl. Phys. B 116, 77 (1976).

[36] K.Guettler et al., Nucl. Phys. B 116, 77 (1976).

[37] J. Schaffner-Bielich, D. Kharzeev, L. McLerran, and R. Venugopalan, Nucl. Phys. A 705,

494 (2002).

[39] B. Back et al., Phys. Rev. C 65, 061901R (2002), pHOBOS Collaboration.

[40] C. Adler et al., Phys. Rev. Lett. 87, 112303 (2001), sTAR Collaboration.

[41] K. Adcox et al., Phys. Rev. Lett. 86, 3500 (2001), pHENIX Collaboration.

[42] B. Back et al., Phys. Rev. Lett. 85, 3100 (2000).

[43] E. Schnedermann, J. Sollfrank, and U. Heinz, Phys. Rev. C 48, 2462 (1993).

[44] S. Esumi, S. Chapman, H. van Hecke, and N. Xu, Phys. Rev. C 55 (1997).

[45] M. van Leeuwen for the NA49 Collaboration, in Proceedings of the XVI International Confer-

ence on Ultrarelativistic Nucleus-Nucleus Collisions, Nantes, France, July 18-24, 2002 (2002),

nucl-ex/0208014, to be published in Nucl. Phys. A.

[46] S. Afanasiev et al., Eur. Phys. J. C 2, 661 (1998).

[47] P. Kolb, Ph.D. thesis, Univ. Regensburg (2001).

[48] J. Sollfrank, P. Koch, and U. Heinz, Phys. Lett. B 252, 256 (1990).

[49] J. Barette et al., Phys. Lett. B 351, 93 (1995).

[50] H. Boggild et al., Z. Phys. C 69, 621 (1996).

[51] U. Wiedemann and U. Heinz, Phys. Rev. C 56, 3265 (1997).

[52] P. Braun-Munzinger, D. Magestro, K. Redlich, and J. Stachel, Phys. Lett. B 518, 41 (2001).

[53] P. F. Kolb, in Proc. 17th Winter Workshop on Nuclear Dynamics, Park City, Utah (2001).

[54] P. F. Kolb, J. Sollfrank, and U. Heinz, Phys. Rev. C 62 (2000).

[55] P. Kolb, P. Huovinen, U. Heinz, and H. Heiselberg, Phys. Lett. B 500, 232 (2001).

[56] D. Teaney, Ph.D. thesis, State University of New York at Stony Brook (2001).

[57] D. Teaney and E. Shuryak, Phys. Rev. Lett. 86, 4783 (2001).

[58] H. Sorge, Phys. Rev. C 52, 3291 (1995).

[59] D. Teaney, J. Lauret, and E. Shuryak (2001), nucl-th/0110037.

[60] W. Broniowski and W. Florkowski, Phys. Rev. Lett. 87, 272302 (2001).

[61] D. Kharzeev and M. Nardi, Phys. Lett. B 507, 121 (2001).

[62] X.-N. Wang and M. Gyulassy, Phys. Rev. Lett. 86, 3496 (2001).

[63] B. Alper et al., Nucl. Phys. B 87 (1975).

[64] T. Alexopoulos et al., Phys. Rev. D 48, 984 (1993).

[66] I. Vitev and M. Gyulassy, Phys. Rev. C 65, 041902 (2002).

[67] B. Kampfer, J. Cleymans, K. Gallmeister, and S. M. Wheaton (Budapest, 2002), pp. 213–222,

hep-ph/0204227.

[68] F. Sikler, Nucl. Phys. A 661, 45c (1999).

[69] V. Freise, Nucl. Phys. A (2002).

[70] W. Broniowski, A. Baran, and W. Florkowski, Acta Phys.Polon. B 33, 4235 (2002).

[71] W. Broniowski and W. Florkowski, Acta Phys.Polon. B 33, 1629 (2002).

Single identified hadron spectra from sNN=130GeV Au+Au collisions

Documents